# GRE Subject Test: Math : Set Theory

## Example Questions

### Example Question #1 : Real Analysis

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

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 : Real Analysis

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

{}

{}

{}

{}

{}

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 #3 : Real Analysis

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

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.

### Example Question #1 : Subsets

What is a subset of ?

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 : Real Analysis

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

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??

All numbers  between  and

All whole numbers

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 : Real Analysis

Which of the following is a finite set?

All whole numbers between  and , inclusive

All real numbers between  and