Real Analysis - GRE Subject Test: Math
Card 0 of 20
What is the value of 
?
What is the value of
When you see a letter with the prime symbol, that means complement. Complement tells you to take whatever is NOT in that set and what is in the universal set. You could also say you are eliminating the numbers in the universal set that are in the set you are complementing.
The universal set is 
Set 
Taking the numbers 7, 8, 9, and 10 out of the universal set you get the answer
When you see a letter with the prime symbol, that means complement. Complement tells you to take whatever is NOT in that set and what is in the universal set. You could also say you are eliminating the numbers in the universal set that are in the set you are complementing.
The universal set is
Set
Taking the numbers 7, 8, 9, and 10 out of the universal set you get the answer
Compare your answer with the correct one above
Evaluate 
Evaluate
The prime symbol means to take the complement of set D. To find a complement, you want to only include the numbers in the universal set that do not appear in the set being complemented.
If set 
and the universal set is 
The numbers you want to include are everything in the universal set except 4, 9, 10, 11, and 12
This leaves the numbers
The prime symbol means to take the complement of set D. To find a complement, you want to only include the numbers in the universal set that do not appear in the set being complemented.
If set
and the universal set is
The numbers you want to include are everything in the universal set except 4, 9, 10, 11, and 12
This leaves the numbers
Compare your answer with the correct one above
Evaluate 
Evaluate
A complement symbol means you want to only include the numbers in the universal set that do not appear in the set being complemented.
However, all the numbers in the universal set appear in itself. This means the complement of ANY universal set is the empty set.
A complement symbol means you want to only include the numbers in the universal set that do not appear in the set being complemented.
However, all the numbers in the universal set appear in itself. This means the complement of ANY universal set is the empty set.
Compare your answer with the correct one above
Evaluate 
Evaluate
Always work in parentheses first. First, you need to solve the union of sets A and B. Union means to include everything in both sets without repeating any duplicates.
Now take the complement of this by including the numbers in the universal set that do not appear in A union B. This leaves
Always work in parentheses first. First, you need to solve the union of sets A and B. Union means to include everything in both sets without repeating any duplicates.
Now take the complement of this by including the numbers in the universal set that do not appear in A union B. This leaves
Compare your answer with the correct one above
If angle 
, find angle 
if angles 
and 
are complementary.
If angle
Step 1: Recall the definition of Complementary angles.
Two angles are complementary if the sum of the two angles is ALWAYS 
.
Step 2: If the sum of the angles is 
, then we can subtract the other one to find the missing angle...
So, 
Step 1: Recall the definition of Complementary angles.
Two angles are complementary if the sum of the two angles is ALWAYS
Step 2: If the sum of the angles is
So,
Compare your answer with the correct one above
Use DeMorgan's law to write a statement that is equivalent to the following statement
Use DeMorgan's law to write a statement that is equivalent to the following statement
The easiest way to remember DeMorgan's law is that you flip the symbol upside down (which changes union to intersection and vice versa), complement both sets (remembering that the complement of a complement is just that set), and either remove parentheses or add parentheses and place the complement symbol outside of it.
Flip the symbol from an intersection to a union, complement both sets, and remove the parentheses.
is equivalent to the original statement
The easiest way to remember DeMorgan's law is that you flip the symbol upside down (which changes union to intersection and vice versa), complement both sets (remembering that the complement of a complement is just that set), and either remove parentheses or add parentheses and place the complement symbol outside of it.
Flip the symbol from an intersection to a union, complement both sets, and remove the parentheses.
Compare your answer with the correct one above
Using DeMorgan's law, which of the following is equivalent to the statement
Using DeMorgan's law, which of the following is equivalent to the statement
The easiest way to remember DeMorgan's law is that you flip the symbol upside down (which changes union to intersection and vice versa), complement both sets (remembering that the complement of a complement is just that set), and either remove parentheses or add parentheses and place the complement symbol outside of it
Flip the intersection symbol to a union, complement both sets, and add parentheses with the complement symbol outside of it.
The easiest way to remember DeMorgan's law is that you flip the symbol upside down (which changes union to intersection and vice versa), complement both sets (remembering that the complement of a complement is just that set), and either remove parentheses or add parentheses and place the complement symbol outside of it
Flip the intersection symbol to a union, complement both sets, and add parentheses with the complement symbol outside of it.
Compare your answer with the correct one above
Using DeMorgan's law, is the statement 
equivalent to 
? If not, choose the correct statement that is equivalent.
Using DeMorgan's law, is the statement
The easiest way to remember DeMorgan's law is that you flip the symbol upside down (which changes union to intersection and vice versa), complement both sets (remembering that the complement of a complement is just that set), and either remove parentheses or add parentheses and place the complement symbol outside of it.
Flip the union symbol to an intersection, complement both sets, add parentheses and a complement symbol outside the parentheses.
The easiest way to remember DeMorgan's law is that you flip the symbol upside down (which changes union to intersection and vice versa), complement both sets (remembering that the complement of a complement is just that set), and either remove parentheses or add parentheses and place the complement symbol outside of it.
Flip the union symbol to an intersection, complement both sets, add parentheses and a complement symbol outside the parentheses.
Compare your answer with the correct one above
Using DeMorgan's law, is the statement 
equivalent to 
? If not, choose the correct statement that is equivalent.
Using DeMorgan's law, is the statement
The easiest way to remember DeMorgan's law is that you flip the symbol upside down (which changes union to intersection and vice versa), complement both sets (remembering that the complement of a complement is just that set), and either remove parentheses or add parentheses and place the complement symbol outside of it.
Flip the union symbol to an intersection symbol, complement both sets, and remove the parentheses
The easiest way to remember DeMorgan's law is that you flip the symbol upside down (which changes union to intersection and vice versa), complement both sets (remembering that the complement of a complement is just that set), and either remove parentheses or add parentheses and place the complement symbol outside of it.
Flip the union symbol to an intersection symbol, complement both sets, and remove the parentheses
Compare your answer with the correct one above
Using DeMorgan's law, which of the following is equivalent to the statement
Using DeMorgan's law, which of the following is equivalent to the statement
The first step is to realize that the C and intersection symbol in the original question are distractions and have nothing to do with applying DeMorgan's Law.
In the parentheses, flip the symbol from an intersection to a union and complement both sets.
Normally, with only two sets, you should eliminate the parentheses that was there to show that the complement symbol applied to the entire parentheses. However, with three sets you still need to know the order in which to work out the problem so you should keep the parentheses around B and A.
The first step is to realize that the C and intersection symbol in the original question are distractions and have nothing to do with applying DeMorgan's Law.
In the parentheses, flip the symbol from an intersection to a union and complement both sets.
Normally, with only two sets, you should eliminate the parentheses that was there to show that the complement symbol applied to the entire parentheses. However, with three sets you still need to know the order in which to work out the problem so you should keep the parentheses around B and A.
Compare your answer with the correct one above
Using DeMorgan's law, is the statement 
equivalent to 
? If not, choose the correct statement that is equivalent.
Using DeMorgan's law, is the statement
The easiest way to remember DeMorgan's law is that you flip the symbol upside down (which changes union to intersection and vice versa), complement both sets (remembering that the complement of a complement is just that set), and either remove parentheses or add parentheses and place the complement symbol outside of it.
Flip the union symbol to an intersection symbol, complement both sets, and remove the parentheses.
The easiest way to remember DeMorgan's law is that you flip the symbol upside down (which changes union to intersection and vice versa), complement both sets (remembering that the complement of a complement is just that set), and either remove parentheses or add parentheses and place the complement symbol outside of it.
Flip the union symbol to an intersection symbol, complement both sets, and remove the parentheses.
Compare your answer with the correct one above
Which of the following sets is not an infinite set??
Which of the following sets is not an infinite set??
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..
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
The set of whole numbers between
Compare your answer with the correct one above
Which of the following is a finite set?
Which of the following is a finite set?
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 
.
Note: The set of real numbers
Step 1: The set of real numbers between two numbers
Step 2: The set of whole numbers between
Compare your answer with the correct one above
Suppose A, B, and C are statements such that C is false if exactly one of A or B is true. If C is true, which of the following is also true?
Suppose A, B, and C are statements such that C is false if exactly one of A or B is true. If C is true, which of the following is also true?
Step 1: Let's break down the logic problem...
C is false if A or B is True.
Example: C-False, A-True, B-False.
Step 2: Try to find what happens if C is true
If C is true, "or" changes to "and", and True becomes false..
So: C-True, A-False, B-False..
A and B must both be false for C to be true..
Answer: Both A and B are False.
Step 1: Let's break down the logic problem...
C is false if A or B is True.
Example: C-False, A-True, B-False.
Step 2: Try to find what happens if C is true
If C is true, "or" changes to "and", and True becomes false..
So: C-True, A-False, B-False..
A and B must both be false for C to be true..
Answer: Both A and B are False.
Compare your answer with the correct one above
Which of the following is true about the relationship between sets?
Which of the following is true about the relationship between sets?
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.
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.
Compare your answer with the correct one above
Which of the following is not a subset of Set A:{ 
}
Which of the following is not a subset of Set A:{
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.
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.
{
Compare your answer with the correct one above
Which of the following is NOT a subset of Set A: 
Which of the following is NOT a subset of Set A:
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 
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 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
Compare your answer with the correct one above
What is a subset of 
?
What is a subset of
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...
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
Compare your answer with the correct one above
Which of the following is a subset of the set: 
?
Which of the following is a subset of the set:
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.
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
Compare your answer with the correct one above
Let 
be the universal set of all people. Let 
be the set of all people who like Band A. Let 
be the set of all people who like Band B. Let 
be the set of all people who like Band C. Let 
stand for Julianna.
Let 
. Which of the following could be true?
Let
Let
, which is the intersection of 
and 
. It follows that 
and 
.
, so it follows that Julianna likes Band A. The three choices that state that she does not can be eliminated.
. This is the union of 
, the complement of 
- that is, the set of people not in 
- and 
. It follows that either Julianna does not like Band B, does like Band C, or both. Therefore, it is not true that she likes Band B and does not like Band C. This can be eliminated.
The only possible choice is that Julianna likes Band A and Band C, but not Band B.
The only possible choice is that Julianna likes Band A and Band C, but not Band B.
Compare your answer with the correct one above