# 3: Sets

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## Meet 3 sets of triplets who graduated from Memorial High School this year

HOUSTON, Texas (KTRK) -- It's not every day you see a set of triplets graduate high school all together, but at Memorial High School in Spring Branch, there are three!

"We've seen each other in classes before and it's kind of special," said Luke Bethancourt.

His brother, Alex, shares the sentiment.

"I think probably the funniest part of the ceremony will be hearing all the triplets' names be called," he said.

This grandfather graduating from Prairie View A&M University is the inspiration we need today and every day.

Of the 664 students that graduated, there were 18 pairs of twins along with the three sets of triplets. Each of them said they're ready for life after high school.

"I think it's going to be very hard for us because we're always together," said Nina Garcia about her two brothers, Alexander and Seth.

"We're all very different, but coming together is special, especially at this school," said Seth.

Plus, you might recognize three of those students, who happen to be the children of ABC13 anchor Gina Gaston and her husband, former Houston Rocket Mario Elie.

Thought they had to juggle raising their children, moving out of state, and working full-time, the Lampkin sisters have a lot to celebrate!

"I don't think she's really ready," said Gina's son, Gaston Elie. It's been quite a year for students as schools were forced to make a change during the pandemic.

Gina's daughter, Lauren Elie, believes it brought her family closer together.

"I think this year with COVID, our relationship as triplets has changed so much because we're all leaving for college. Like, 'OK, this time is so good for us especially, for our parents, too,'" she said.

As they crossed the stage, the siblings said they're excited for what their future holds.

"Everything I've experienced now, I've had [Gaston and Lauren] to lean on but now it's just me on my own," said Glenn Elie.

## Cluster Sets Explained

Cluster sets are smaller sets built-in a larger set with rest increments that range from 10-30 seconds. When you typically think of a set, you think of doing one rep immediately after another until you complete all of the prescribed reps. Clusters sets look like this: Do three reps, rest 30 seconds, do three reps, rest 30 seconds, do three reps. That entire sequence is one set.

The main benefit of cluster sets is that you can lift more weight for the same overall volume. If you were to do deadlifts for a straight-set of eight reps, you could only lift with, say, 75 percent of your one-rep max (1RM). But, breaking that set up into four clusters of two reps allows you to use closer to 90 percent of your 1RM for the same amount of overall volume. For that reason, it’s a popular technique among strength athletes such as powerlifters.

## 1st Place JAMEZ

### How Much Rest Is Best?

The "best" amount of time to rest between sets, like most things in bodybuilding, depends on what specific goal you're training for.

Do you want to be stronger, more muscular or increase your stamina? Common sense and research tells us that we can only pursue one goal at a time.

If we want to be stronger, we should follow a training program that increases our strength as quickly as possible. Likewise for size and stamina. Not surprisingly, with each specialized program comes a different requirement for rest periods.

Let's look at WHAT those different rest periods are and, most importantly, explore WHY they are.

### Strength Training

To get stronger faster, the best rest period is 3 to 5 minutes between sets.

This is because much of the energy your body consumes during traditional strength training (heavy weight, 1 to 6 reps) comes from the Adenosine Triphosphate Phosphocreatine system. The ATP-PC system uses phosphagens to produce energy very quickly and without the use of oxygen. Your body has a very small phosphagen reserve, which lasts about 15 seconds. It takes your body about 3 minutes to fully replenish phosphagen stores (Fleck, 1983).

In other words, if you give your ATP-PC system at least 3 minutes to recharge, you'll lift more weight and get stronger faster.

In one study, athletes lifted a weight more times in 3 sets after resting 3 minutes compared to when they rested only 1 minute (Kraemer, 1997). Another study showed a 7% increase in squat strength after 5 weeks of training with 3 minute rest periods.

The group that rested for 30 seconds only improved their squat by 2% (Robinson et al, 1995). Two more studies that examined very short rest periods (30 to 40 seconds) found they caused nowhere near the strength gains from longer rest periods (Kraemer et al, 1987 Kraemer, 1997).

You'll cool down too much if you rest longer than 5 minutes. No-one wants to increase their chances of injury.

### Hypertrophy Training

To get bigger quicker, the best rest period is 1 to 2 minutes between sets.

Typical bodybuilding/hypertrophy training (moderate-heavy weight, 6-12 reps) draws energy from the ATP-PC and glycolytic system (the glycolytic system gets most of its energy from the carbs you eat). The aerobic metabolism plays a very small part as well.

Think of the ATP-PC system as a racehorse and the glycolytic system as a steady, dependable Clydesdale. Because your glycolytic system has come to the party, your body doesn't need to rest as long between sets as when you're strength training.

Bodybuilders take advantage of shorter rest periods to make their muscles BIGGER. How? Well, one of the key factors in how much muscles grow is the amount of anabolic hormones your body produces after weight training (McCall et al, 1999). Short rest periods of between 1 and 2 minutes cause a greater release of these hormones than longer rest periods (Kraemer et al, 1991 Kraemer et al, 1990).

Short rest periods also cause other muscle-building bonuses like increased lactate production and blood flow to the targeted muscles (Kraemer, 1997 Kraemer et al, 1987). Don't laugh about the blood flow bit. I know it sounds like old-school "pump" talk. But it's been shown that the increased blood flow to your muscles helps the protein get there quicker (Biolo et al, 1995).

Muscle fatigue, caused by lactate production, has also been implicated in short-term strength gains and significant hypertrophy (Rooney et al, 1994).

### Endurance Training

To increase muscular endurance as quickly as possible, the best rest period is 45 seconds to 2 minutes between sets.

Classic endurance training (light-moderate weight, 15-20 reps) draws much of its energy from aerobic metabolism. This means your body burns carbs and fats in the presence of oxygen.

Basically, endurance training is aimed at making your muscles more resistant to fatigue. Without going into complicated details, a major cause of fatigue in endurance activities is lactic acid build-up. Regularly lifting weights in a 15-20RM makes your body more efficient at clearing lactic acid from the muscles by boosting your body's hormonal and vascular systems (Donovan & Brooks, 1983).

Coaches from a variety of endurance-related sports usually recommend a 1:1 or 1:2 work-rest interval to increase your body's lactate threshold (Sleamaker & Browning, Winbourne, 1998, Horswill, 1992). A strict set of 15 to 20 reps should take you between 45 seconds and 1 minute to complete… which works out to a rest period of between 45 seconds and 2 minutes.

And here's a final interesting fact: bodybuilders (who train with short rest periods and high reps) are more fatigue-resistant than powerlifters (long rest, low reps)(Kraemer, 1987). Bodybuilders are better at clearing lactic acid.

### Bonus Question

I've done a number of things over the years to crank up training intensity. Strips sets, endurance training…all things that require you to rest for short periods of time (or not rest at all!).

But the most intense "short rest" workout I've ever done was Bahlow Circuit Training… I almost barfed. And let's not forget. barfing is actually a BAD thing and not something you ever want to do after a workout.

BCT is not for the faint hearted. It requires bucketloads of protein and many hours of sleep afterwards. I did BCT for six weeks and made newbie-like gains… but it's hard, hard work.

BCT is basically a giant circuit of supersets. Make that super-supersets. You have three exercises per bodypart that you do in a row without rest. The exercises start hard and end with an "easier" movement. Here's an example using the leg superset:

You work out your 10RM on each exercise BEFORE you do the circuit. That's bad. Because by the time you've done squats and deadlifts without a break, your 10RM on leg press feels like a 5 rep max. And you're expected to crank out 10.

Bodyparts worked are legs, chest, back, shoulders and arms. You get a two minute rest between each megaset. TWO MINUTES. You do 3 circuits.

First time I did BCT I was on the floor afterwards. Looking at the bright lights. It's the closest I have ever come to barfing after a workout.

##### References
1. Biolo, G et al. Increased rates of muscle protein turnover and amino acid transport after resistance exercise in humans.Am. J. Physiol. 268: E514-E520, 1995
2. Donovan, C and G Brooks. Endurance training affects lactate clearance, not lactate production.Am. J. Physiol. 244: E83-E92, 1983.
3. Fleck, S. Bridging the gap: interval training physiological basis. NSCA J. 5: 40, 57-62, 1983.
4. Horswill, C.A. Interval training for wrestlers. Wrestling USA, Sept. 15, 1992
5. Kraemer, W. A series of studies-the physiological basis for strength training in American football: fact over philosophy.J. Strength Cond. Res. 11:131-142, 1997.
6. Kraemer, W et al. Endogenous anabolic hormonal and growth factor responses to heavy resistance exercise in males and females. Int. J. Sports Med. 12:228-235, 1991.
7. Kraemer, W et al. Hormonal and growth factor responses to heavy resistance exercise protocols.J. Appl. Physiol. 69:1442-1450, 1990.
8. Kraemer, W et al. Physiologic responses to heavy-resistance exercise with very short rest periods.Int. J. Sports Med. 8:247-252, 1987.
9. McCall, G et al. Acute and chronic hormonal responses to resistance training designed to promote muscle hypertrophy.Can. J. Appl. Physiol. 24:96-107, 1999.
10. Robinson, J et al. Effects of different weight training exercise/rest intervals on strength, power, and high intensity exercise endurance.J. Strength Cond. Res. 9:216-221, 1995.
11. Sleamaker, R and R Browning. Serious Training for Endurance Athletes. 2nd ed. Human Kinetics, 1996.

#### Topic Of The Week

Topic of the Week gives forum members the chance to share their knowledge with the world!

## The odds of having twins

Non-identical twins are about twice as common as identical twins. The incidence of non-identicals in the UK is one in 112 births, compared with one in 227 births for identicals.

Identical twins are down to chance: one egg is fertilised, but it then divides. Fraternal twins happen when a woman produces two eggs, and both are fertilised. So with identical twins the DNA makeup is exactly the same in each twin with fraternal twins, the DNA is no more similar than in any two siblings.

A history of non-identical twins on the mother's side increases her chance of twins and a woman who already has twins has four times the normal chance of having them again in a subsequent pregnancy.

Increased maternal age makes twins more likely, because older ovaries are more likely to release two eggs in the same month.

The odds of having three sets of non-identical twins is about one in 88,000, but the chance of having three sets of identical twins is one in 11.7m.

Below is a list of Necromancer Legendary Set items. A majority of these items will only drop from killing monsters, opening chests, and destroying/clicking lootable items on the Torment difficulty levels, but also can be won from Kadala through Blood Shard gambling.

Although these set items are intended for Necromancers, some of these items can be equipped by other classes. Keep in mind, however, that other classes will not gain any ability bonuses from these set items.

### Bones of Rathma Set Dungeon

The Dungeon of the Bones of Rathma is located in The Sacred Path in Act 2. Go to the Temple of the Firstborn. Then, go through the door to The Sacred Path. Next, follow the path down towards the exit to Shrouded Moors and the entrance to the dungeon is just to the left before the exit.

• Your minions have a chance to reduce the cooldown of Army of the Dead by 1 second each time they deal damage.

### Grace of Inarius Set Dungeon

The Dungeon of the Grace of Inarius is located in The Drowned Temple in Act 1. Once inside the temple, head down the stairs. At the bottom, look for the entrance just ahead.

• Bone Armor also activates a swirling tornado of bone, damaging nearby enemies for 750% weapon damage and increasing the damage they take from the Necromancer by 2750%

### Pestilence Master's Shroud Set Dungeon

The Dungeon of the Pestilence Master's Shroud is located in Bastion Keep's Stronghold on Level 3 in Act 3. Upon arriving on Level 3, continue forward until a pathway to the right appears. Follow this path to eventually reach the dungeon entrance.

• Each enemy you hit with a Bone Spear reduces your damage taken by 2%, up to a maximum of 50%. Lasts 15 seconds.
• Each corpse you consume grants you and Empowered Bone Spear charge that increases the damage of your next Bone Spear by 3000%

### Trag'Oul's Avatar Set Dungeon

The Dungeon of Trag'Oul's Avatar is located in the Upper Realm of Cursed Fate in Act 4. Upon arriving, head right. Then, turn to head down. After a short while, you'll reach the entrance.

## 3 Sets of Chabad Twins Born Today

3 Chabad couples from Crown Heights, East Flatbush and the Five Towns were blessed with sets of twins on Sunday.

The news comes a day after Yud Shvat, an auspicious day in the Chabad calendar as the yartzeit of the Frierdiker Rebbe and when the Rebbe assumed leadership of Chabad-Lubavitch.

According to data collected by the Centers for Disease Control, there were 133,155 twins born in the United States in 2015, according to the website verywellfamily.com. That’s 33.5 per 1,000 live births, or put another way, about 3.35% of live births.

The rate of multiple births increased and peaked during the 1990s but has been declining over the past decade, they said.

Such multiple births have not happened in the Chabad community in a while, according to COLlive’s Mazal Tov records.

The families who have double additions of blessings are:

Twin girls to Mendel and Perl Groner (nee Faygen) – Crown Heights
Twin boys to Yitzchok and Chana Rivka Wiener (nee Lewis) – Lawrence, NY
Twin girls to Yoni and Sarochel Sarue – East Flatbush, NY

## 3: Sets

Readings for Session 5 – (Continued)

Complement and Set Difference

Remember that we often work with a specific set of objects when solving problems or discussing issues. We called this set of objects a universal set or universe. For example, in the lead-in problem above, the universal set could be either the set of all U. S. dollars or the set of the $836 Sam originally had in the checking account. Complement of a Set: The complement of a set, denoted A ' , is the set of all elements in the given universal set U that are not in A . The Venn diagram for the complement of set A is shown below where the shaded region represents A ' . Example: For the lead-in example on the previous page, let the universal set U be the$836 Sam originally has in the checking account and let A be the set of the $429 of the check. The complement of set A would be the set of the$407 remaining in the checking account.

Example: U ' = ∅ The complement of the universe is the empty set.

Example: ∅ ' = U The complement of an empty set is the universal set.

Set Difference: The relative complement or set difference of sets A and B, denoted AB, is the set of all elements in A that are not in B .

The Venn diagram for the set difference of sets A and B is shown below where the shaded region represents AB.

Example: For the lead-in example on the previous page, let the universal set U be the set of all U.S. dollars, let set A be the set of $836 Sam originally has in the checking account, and let B be the set of the$429 of the check. Then the set difference of A and B would be the \$407 remaining in the checking account.

Example: Let A = <a, b, c, d> and B = <b, d, e>. Then AB = <a, c> and BA = <e>.

Example: Let G = <t, a, n> and H = <n, a, t>. Then GH = ∅ .

How should we define the subtraction of whole numbers?

In the lead-in example on an earlier page of this section, the remaining balance was the difference between the cardinalities of the sets for the checking account and the check. This also works for the third example (above)where

n(G) – n(H) = 3 – 3 = 0 = n( ∅ ).

But, with the second example (above) the difference between the cardinalities does not give the expected result, e.g.,

n(A) – n(B) = 4 – 3 = 1 ≠ 2 = n(AB).

In this case, B is not a subset of A. This leads to the set definition for subtraction of whole numbers given on the next page.

## 7 Formulas for Tackling Three Overlapping Sets on the GMAT

Venn diagram problems are a staple of the GMAT word problems repertoire, and while people are generally familiar with the 2-set venn diagram formulas, the 3-set venn diagram equations often pose a challenge for test-takers. In a previous post, we saw how to solve three overlapping sets questions using venn diagrams. Today, we will look at all of the various venn diagram formulas floating around on three overlapping sets. Most of these are self explanatory but we will look into the details of the less commonly known three-set venn formulas.

There are two basic 3-set venn diagram formulas that we already know:

1) Total = n(No Set) + n(Exactly one set) + n(Exactly two sets) + n(Exactly three sets)

2) Total = n(A) + n(B) + n(C) – n(A and B) – n(B and C) – n(C and A) + n(A and B and C) + n(No Set)

From these two standard venn formulas, we can derive all the other three-set venn formula offshoots:

n(Exactly one set) + n(Exactly two sets) + n(Exactly three sets) gives us n(At least one set). So we get:

3) Total = n(No Set) + n(At least one set)

From (3), we get n(At least one set) = Total – n(No Set)

Plugging this into (2), we then get:

4) n(At least one set) = n(A) + n(B) + n(C) – n(A and B) – n(B and C) – n(C and A) + n(A and B and C)

Now let’s see how we can calculate the number of people in exactly two sets. There is a reason we jumped to n(Exactly two sets) instead of following the more logical next step of figuring out n(At least two sets) – it will be more intuitive to get n(At least two sets) after we find n(Exactly two sets).

n(A and B) includes people who are in both A and B and it also includes people who are in A, B and C. Because of this, we should remove n(A and B and C) from n(A and B) to get n(A and B only). Similarly, you get n(B and C only) and n(C and A only), so adding all these three will give us number of people in exactly 2 sets.

n(Exactly two sets) = n(A and B) – n(A and B and C) + n(B and C) – n(A and B and C) + n(C and A) – n(A and B and C). Therefore:

5) n(Exactly two sets) = n(A and B) + n(B and C) + n(C and A) – 3*n(A and B and C)

Now we can easily get n(At least two sets):

6) n(At least two sets) = n(A and B) + n(B and C) + n(C and A) – 2*n(A and B and C)

This is just n(A and B and C) more than n(Exactly two sets). That makes sense, doesn’t it? Here, you include the people who are in all three sets once and n(Exactly two sets) converts to n(At least two sets)!

Now, we go on to find n(Exactly one set). From n(At least one set), let’s subtract n(At least two sets) i.e. we subtract (6) from (4)

n(Exactly one set) = n(At least one set) – n(At least two sets), therefore:

7) n(Exactly one set) = n(A) + n(B) + n(C) – 2*n(A and B) – 2*n(B and C) – 2*n(C and A) + 3*n(A and B and C)

You don’t need to learn all these formulas. Just focus on first two and know how you can arrive at the others if required. Let’s try this in an example problem:

Among 250 viewers interviewed who watch at least one of the three TV channels namely A, B &C. 116 watch A, 127 watch C, while 107 watch B. If 50 watch exactly two channels. How many watch exactly one channel?

n(At least one channel) = 250

n(Exactly two channels) = 50

So we know that n(At least one channel) = n(Exactly 1 channel) + n(Exactly 2 channels) + n(Exactly 3 channels) = 250

250 = n(Exactly 1 channel) + 50 + n(Exactly 3 channels)

Let’s find the value of n(Exactly 3 channels) = x

We also know that n(At least one channel) = n(A) + n(B) + n(C) – n(A and B) – n(B and C) – n(C and A) + n(A and B and C) = 250

Also, n(Exactly two channels) = n(A and B) + n(B and C) + n(C and A) – 3*n(A and B and C)

So n(A and B) + n(B and C) + n(C and A) = n(Exactly two channels) + 3*n(A and B and C)

Plugging this into the equation above:

250 = n(A) + n(B) + n(C) – n(Exactly two channels) – 3*x + x

250 = 116 + 127 + 107 – 50 – 2x

250 = n(Exactly 1 channel) + 50 + 25

As you can see, fluency with the triple-set venn diagram formulas can be an important skill for GMAT quantitative mastery. It is also critically important on 3-set venn problems to read carefully, as the difference between “at least two” and “exactly two,” for example, is a small change in diction but a massive change in the correct answer. This of course is also true on 2-set venn diagram problems, although the 3-set venn variety just offers even more permutations on how information can be provided and questions can be asked.

Importantly, make sure you know the most standard 3-set venn diagram formulas (the first two on this list) as they are the foundation for all the other 3-set formulas and they’re very difficult and time-consuming to try to “teach yourself” on test day. It’s also extremely helpful to be familiar with the other 3-set formulas from this post so that even if you don’t have them memorized, you’ve seen them and can derive them as necessary from the must-know 3-set venn formulas at the top of the list.

Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America (wait, could that in and of itself be a 3-set venn diagram problem setup?). She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!

## 3 Piece Bedroom Sets

The 3 piece bedroom set is the simplest way to furnish a bedroom completely. These sets include everything you need to move straight in and get some quality nap time- a stylish and practical nightstand, a dresser for clothes and accessories, and, of course, a comfortable and tempting bed.

Beds in 3 bedroom sets come in a range of styles. Tall headboards in dark woods contrast beautifully with pale walls or a neutral color scheme. Lower platform beds create the illusion of additional space, or leave more wall space free for your favorite art.

Storage is a quick win with a 3 piece bedroom set. Rustic nightstands with two or three drawers hide away your favorite trinkets. Or go for a modern set with a sleek dresser built to store all your clothes and display a few photos proudly.