GRE Subject Test: Math : Real Analysis

Study concepts, example questions & explanations for GRE Subject Test: Math

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Example Questions

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Example Question #1 : Set Theory

Which of the following is true about the relationship between sets?

 

Possible Answers:

Correct answer:

Explanation:

The subset symbol should be read as "is a subset of" So it's the first letter is a subset of the second letter. To be a subset, all of its elements must be contained in the other set.

The only one of these relationships that is true (where the entire set on the left is in the right set) is

The elements of B, 4, 5, 6, and 8 all appear in set D.

Example Question #2 : Set Theory

Which of the following is not a subset of Set A:{ }

Possible Answers:

{}

{}

{}

{}

Correct answer:

{}

Explanation:

Step 1: A subset of a set must have elements in Set A. If any number in the subset is not in the original set, then that subset is not a subset of that set.

{} is not a subset because  is not in Set A.

Example Question #1 : Subsets

Which of the following is NOT  a subset of Set A: 

Possible Answers:

 

Correct answer:

Explanation:

Step 1: Recall the definition of a subset. A subset is a small part of a bigger given set; ALL numbers in the subset must be in the original set.

Step 2: We look at the original set and then look at the answers. If there is any answer that has an element that is not showing up in the original set, than that is the right answer.

Let's look at: . The  is in the original set, but the  is not. Since we have a number in the subset that is not in the original set, we can say that  is not a subset.

The other two answers with brackets are subsets of the original set. All elements in the subsets are present in the original set.

The empty set is always a subset of any given set. 

The answer is 

Example Question #1 : Subsets

What is a subset of ?

Possible Answers:

Correct answer:

Explanation:

Step 1: Define a subset. A subset of a bigger set is a smaller part where all the elements in the subset must be present in the bigger set.

 The answer is . All numbers in this subset are in the bigger set, which is provided in the question...

Example Question #5 : Set Theory

Which of the following is a subset of the set: ?

Possible Answers:

Correct answer:

Explanation:

Step 1: Define a subset

A subset of a big set is a set that has some of the elements that are in the bigger parent set.

The answer is  because both  and  are both in the bigger set.

Example Question #1 : Set Theory

Which of the following sets is not an infinite set??

Possible Answers:

All numbers  between  and 

All whole numbers

Correct answer:

All whole numbers

Explanation:

Step 1: Determine the difference between Infinite and Finite Sets...

Finite Sets: A set that has very limited elements in it
Infinite Sets: Any set where I can always find another number between two given boundaries.

The Set of integers and rational numbers are infinite sets..
All numbers between  and  is also an infinite set because I can come up with infinite decimal numbers..

The set of whole numbers between  and  inclusive is a finite set because I ask for a specific type of number.. a whole number. Whole numbers cannot be decimals..

Example Question #1 : Set Theory

Which of the following is a finite set?

Possible Answers:

All whole numbers between  and , inclusive

All real numbers between  and 

Correct answer:

All whole numbers between  and , inclusive

Explanation:

Note: The set of real numbers , natural numbers  are both infinite sets.
Step 1: The set of real numbers between two numbers  is also an infinite set.

Step 2: The set of whole numbers between  and  inclusive is finite because there are only three numbers that are represented by the set. These numbers are .

Example Question #1 : Relations

What is ?

Possible Answers:

Correct answer:

Explanation:

means the intersection of set A and set C. Intersection means that you want to choose only the numbers that are in BOTH set A and set C. The only numbers that are in common to those two sets are 3 and 9.

Example Question #1 : Union & Intersect

What is ?

Possible Answers:

Correct answer:

Explanation:

means the union of set B and set C. Union means to include all the numbers that are in either set B or set C (without listing duplicates twice). The numbers 1, 3, 5, 8, 9, and 11 appear in B and the numbers 2, 3, 5, 6, 9, 12 appear in C. Including all of those numbers in the set symbol gives the correct answer.

Example Question #11 : Understanding Sets

Let universal set  be the set of all people. Let  represent Brittany. 

Let  be the set of people who like James Blunt, , the set of people who like John Legend, and , the set of people who like Pharrell Williams.

True or false: Brittany likes James Blunt, John Legend, and Pharrell Williams.

Statement 1: 

Statement 2: 

Possible Answers:

EITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question. 

Correct answer:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Explanation:

Assume Statement 1 alone.  is the intersection of the sets , and . Since Brittany falls in this intersection, she falls in all three sets, and it follows that she likes all three of James Blunt, John Legend, and Pharrell Williams.

Assume Statement 2 alone.  is the union of the three sets. Since Brittany falls in this union, she falls in one, two, or all three sets, which means that she likes at least one of James Blunt, John Legend, and Pharrell Williams. However, more information is needed before it can be established whether or not she likes all three.

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