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GRE Subject Test: Math : Complements

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

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Example Questions

Example Question #1 : Complements

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

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

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

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

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

What is the value of C{}' ?

Possible Answers:

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

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

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

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

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

Correct answer:

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

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

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

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Example Question #132 : Other Topics

$U=\left \{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\right \}$

$A=\left \{ 3, 4, 6, 7, 8, 9\right \}$

$B=\left \{ 1, 3, 4, 5\right \}$

$C=\left \{ 2, 7, 8, 9, 11, 12\right \}$

$D=\left \{ 4, 9, 11, 12\right \}$

Evaluate

Possible Answers:

$D'=\left \{ 4, 9, 11, 12\right \}$

$D'=\left \{ 3, 4, 6, 7, 10, 11\right \}$

$D'=\left \{ 1, 2, 3, 5, 6, 7, 8, 10\right \}$

$D'=\left \{ 1, 2, 5, 10, 11, 12\right \}$

Correct answer:

$D'=\left \{ 1, 2, 3, 5, 6, 7, 8, 10\right \}$

Explanation:

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 $D=\left \{ 4, 9, 11, 12\right \}$

and the universal set is $U=\left \{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\right \}$

The numbers you want to include are everything in the universal set except 4, 9, 10, 11, and 12

This leaves the numbers

$D'=\left \{ 1, 2, 3, 5, 6, 7, 8, 10\right \}$

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Example Question #21 : Real Analysis

$U=\left \{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\right \}$

$A=\left \{ 3, 4, 6, 7, 8, 9\right \}$

$B=\left \{ 1, 3, 4, 5\right \}$

$C=\left \{ 2, 7, 8, 9, 11, 12\right \}$

$D=\left \{ 4, 9, 11, 12\right \}$

Evaluate

Possible Answers:

$U'=\left \{ 2, 5, 8, 10\right \}$

$U'=\left \{ \right \}$

$U'=\left \{ 3, 4, 7, 8, 9, 11, 12\right \}$

$U'=\left \{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\right \}$

$U'=\left \{ 10\right \}$

Correct answer:

$U'=\left \{ \right \}$

Explanation:

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.

$\left \{ \right \}$

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Example Question #141 : Other Topics

$U=\left \{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\right \}$

$A=\left \{ 3, 4, 6, 7, 8, 9\right \}$

$B=\left \{ 1, 3, 4, 5\right \}$

$C=\left \{ 2, 7, 8, 9, 11, 12\right \}$

$D=\left \{ 4, 9, 11, 12\right \}$

Evaluate $\left ( A\cup B\right )'$

Possible Answers:

$(A \cup B)'=\left \{ 2, 10, 11, 12\right \}$

$\left ( A\cup B\right )'=\left \{ 1, 5, 6, 7, 8, 9\right \}$

$\left ( A\cup B\right )'=\left \{ 1, 3, 4, 5, 6, 7, 8, 9\right \}$

$\left ( A\cup B\right )'=\left \{ 1, 2, 5, 6, 7, 8, 9, 10, 11, 12\right \}$

$\left ( A\cup B\right )'=\left \{ 3, 4\right \}$

Correct answer:

$(A \cup B)'=\left \{ 2, 10, 11, 12\right \}$

Explanation:

$\left ( A \cup B\right )'$

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.

$A\cup B=\left \{ 1, 3, 4, 5, 6, 7, 8, 9\right \}$

Now take the complement of this by including the numbers in the universal set that do not appear in A union B. This leaves

$(A \cup B)'=\left \{ 2, 10, 11, 12\right \}$

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Example Question #2 : Complements

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

Possible Answers:

$54.441^{\circ}$

$54.422^{\circ}$

$54.4421^{\circ}$

$54.4^{\circ}$

Correct answer:

$54.422^{\circ}$

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

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GRE Subject Test: Math : Complements

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

All GRE Subject Test: Math Resources

Example Questions

Example Question #1 : Complements

Example Question #132 : Other Topics

Example Question #21 : Real Analysis

Example Question #141 : Other Topics

Example Question #2 : Complements

All GRE Subject Test: Math Resources

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