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GRE Quantitative Reasoning › Relations

Questions 1 - 10

If angle $A=35.578^{\circ}$ , find angle if angles and are complementary.

$54.422^{\circ}$

$54.441^{\circ}$

$54.4421^{\circ}$

$54.4^{\circ}$

Explanation

Step 1: Recall the definition of Complementary angles.

Two angles are complementary if the sum of the two angles is ALWAYS $90^{\circ}$ .

Step 2: If the sum of the angles is $90^{\circ}$ , then we can subtract the other one to find the missing angle...

So, $B=(90-35.578)^{\circ}=54.422^{\circ}$

If angle $A=35.578^{\circ}$ , find angle if angles and are complementary.

$54.422^{\circ}$

$54.441^{\circ}$

$54.4421^{\circ}$

$54.4^{\circ}$

Explanation

Step 1: Recall the definition of Complementary angles.

Two angles are complementary if the sum of the two angles is ALWAYS $90^{\circ}$ .

Step 2: If the sum of the angles is $90^{\circ}$ , then we can subtract the other one to find the missing angle...

So, $B=(90-35.578)^{\circ}=54.422^{\circ}$

Using DeMorgan's law, is the statement $(A' \cup C)'$ equivalent to $A \cap C$ ? If not, choose the correct statement that is equivalent.

No, the equivalent statement is $A \cap C'$

Yes, the statements are equivalent.

No, the equivalent statement is $A \cup C'$

No, the equivalent statement is $(A \cup C)'$

No, the equivalent statement is $(A \cap C')'$

Explanation

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.

$(A' \cup C)'$

Flip the union symbol to an intersection symbol, complement both sets, and remove the parentheses

$A \cap C'$

Using DeMorgan's law, is the statement $(A' \cup C)'$ equivalent to $A \cap C$ ? If not, choose the correct statement that is equivalent.

No, the equivalent statement is $A \cap C'$

Yes, the statements are equivalent.

No, the equivalent statement is $A \cup C'$

No, the equivalent statement is $(A \cup C)'$

No, the equivalent statement is $(A \cap C')'$

Explanation

$(A' \cup C)'$

Flip the union symbol to an intersection symbol, complement both sets, and remove the parentheses

$A \cap C'$

What is the union of the following sets:

Set A={}
Set B={}

{}

None of the Above

Explanation

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 ( $A \cup B$ ) is {}

What is the union of the following sets:

Set A={}
Set B={}

{}

None of the Above

Explanation

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 ( $A \cup B$ ) is {}

$U=\left { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \right }$

$A=\left { 4, 9 \right }$

$B=\left { 1, 3, 5, 10 \right }$

$C=\left { 7, 8, 9, 10 \right }$

$D=\left { 1, 3, 5, 10 \right }$

What is the value of ?

$\left { 1, 2, 3, 4, 5, 6 \right }$

$\left { 1, 3, 5, 10 \right }$

$\left { 1, 2, 3, 5, 6, 8, 10 \right }$

$\left { 1, 3, 4, 5, 9, 10 \right }$

$\left {7, 8, 9, 10 \right }$

Explanation

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 $U=\left { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \right }$

Set $C=\left { 7, 8, 9, 10 \right }$

Taking the numbers 7, 8, 9, and 10 out of the universal set you get the answer

$\left { 1, 2, 3, 4, 5, 6 \right }$

$U=\left { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \right }$

$A=\left { 4, 9 \right }$

$B=\left { 1, 3, 5, 10 \right }$

$C=\left { 7, 8, 9, 10 \right }$

$D=\left { 1, 3, 5, 10 \right }$

What is the value of ?

$\left { 1, 2, 3, 4, 5, 6 \right }$

$\left { 1, 3, 5, 10 \right }$

$\left { 1, 2, 3, 5, 6, 8, 10 \right }$

$\left { 1, 3, 4, 5, 9, 10 \right }$

$\left {7, 8, 9, 10 \right }$

Explanation

The universal set is $U=\left { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \right }$

Set $C=\left { 7, 8, 9, 10 \right }$

Taking the numbers 7, 8, 9, and 10 out of the universal set you get the answer

$\left { 1, 2, 3, 4, 5, 6 \right }$

$A=\left { 3, 4, 7, 9 \right }$

$B=\left { 1, 3, 5, 8, 9, 11 \right }$

$C=\left { 2, 3, 5, 6, 9, 12 \right }$

What is $B \cup C$ ?

$\left { 1, 2, 3, 5, 6, 8, 9, 11, 12\right }$

$\left { 3, 5, 9 \right }$

$\left { 3 \right }$

$\left { 1, 3, 4, 5, 7, 8, 9, 11 \right }$

$\left { \right }$

Explanation

$B \cup C$ 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.