Relations - GRE Quantitative Reasoning
Card 0 of 96
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
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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
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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.
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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
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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,
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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.
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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.
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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.
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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
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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.
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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.
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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.
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Let be the universal set of all people. Let 
be the set of all people who are dancers and 
be the set of all people that are singers.
Let 
represent Jeremy. Which of these statements states the opposite of "Jeremy is not a dancer, but he is a singer" in set notation?
Let
Let
In set notation, "Jeremy is not a dancer, but he is a singer" can be stated as
That is, Jeremy falls in the intersection of the complement of the set of dancers 
and the set of singers 
.
The opposite of this is that 
is in the complement of this set:
By DeMorgan's law, this is equivalent to saying
, or
.
In set notation, "Jeremy is not a dancer, but he is a singer" can be stated as
That is, Jeremy falls in the intersection of the complement of the set of dancers
The opposite of this is that
By DeMorgan's law, this is equivalent to saying
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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: 
Let universal set
Let
True or false: Brittany likes James Blunt, John Legend, and Pharrell Williams.
Statement 1:
Statement 2:
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.
Assume Statement 1 alone.
Assume Statement 2 alone.
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What is 
?
What is
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.
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What is 
?
What is
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.
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What is the intersection of :
Set A={
}
Set B={
}
What is the intersection of :
Set A={
Set B={
Step 1: Recall the definition for intersection of two sets: The intersection of two sets is a subset that has numbers that is shared between two sets, A and B.
Step 2: Find the shared elements between both sets
Set A and Set B both share 4,11, and 14.
The intersection of both sets is {
}
Step 1: Recall the definition for intersection of two sets: The intersection of two sets is a subset that has numbers that is shared between two sets, A and B.
Step 2: Find the shared elements between both sets
Set A and Set B both share 4,11, and 14.
The intersection of both sets is {
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What is the union of the following sets:
Set A={
}
Set B={
}
What is the union of the following sets:
Set A={
Set B={
Step 1: Define the union of two sets. The union of two sets is all elements that are in two sets, as well as the elements that are shared.
Step 2: Find the union of the sets:
Set A has elements: 
Set B has elements: 
Union of Set A and B (
) is {
}
Step 1: Define the union of two sets. The union of two sets is all elements that are in two sets, as well as the elements that are shared.
Step 2: Find the union of the sets:
Set A has elements:
Set B has elements:
Union of Set A and B (
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What is the intersection of Set A: 
and Set B: 
What is the intersection of Set A:
Step 1: Define what the intersection of two sets means.. The intersection of two sets is defined as a set that has elements that are shared between both original sets..
Step 2: Find any shared elements..
If we look, Set A and Set B do not share any elements..
Therefore, there is no intersection of the two sets.
Step 1: Define what the intersection of two sets means.. The intersection of two sets is defined as a set that has elements that are shared between both original sets..
Step 2: Find any shared elements..
If we look, Set A and Set B do not share any elements..
Therefore, there is no intersection of the two sets.
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Evaluate 
Evaluate
This question asks you to find the intersection of the sets B and D. Include only the numbers that both sets have in common with one another. The only common number with both sets is 4.
This question asks you to find the intersection of the sets B and D. Include only the numbers that both sets have in common with one another. The only common number with both sets is 4.
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