Set Theory → Complements & Differences

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Cierra Henderson, MBA |
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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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| Attempts: 17 | Questions: 10 | Updated: Jan 21, 2026
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Question 1 / 11
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1) If U={a,b,c,d,e} and B={b,d,e}, find B′.

Explanation

Complement = elements in U but not in B → {a,c}.

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About This Quiz
Set Theory Complements & Differences - Quiz

What’s in one set but not the other? Complements and differences reveal those hidden details. In this quiz, you’ll practice applying these operations to different scenarios. Take this quiz to sharpen your set reasoning toolkit.

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2) If A={1,2,3,4} and B={3,4,5,6}, find A−B.

Explanation

Elements in A not in B → {1,2}.

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3) If U={1,2,3,4} and A={1,4}, find A′−A.

Explanation

A′={2,3}. Subtracting A doesn’t remove anything further, so {2,3}.

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4) If U={1,2,3,4,5,6} and A={1,2,3}, find A′.

Explanation

The complement contains everything in U not in A → {4,5,6}.

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5) If U={1,2,3,4,5,6} and A=U, find A′.

Explanation

Complement of the universal set is empty.

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6) If A={m,n,o,p} and B={o,p,q,r}, find A−B.

Explanation

Only m and n are in A but not in B.

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7) If A={1,2,3} and B={2,3,4}, find B−A.

Explanation

Only 4 is in B but not in A.

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8) If U={a,b,c,d} and A={a,b}, find (A′)′.

Explanation

Double complement gives back the original set.

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9) If A={x,y,z} and B={y,z}, find B−A.

Explanation

All elements of B are in A, so the difference is empty.

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10) If U={1,2,3,4,5} and A=∅, find A′.

Explanation

Complement of the empty set is the universal set.

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Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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If U={a,b,c,d,e} and B={b,d,e}, find B′.
If A={1,2,3,4} and B={3,4,5,6}, find A−B.
If U={1,2,3,4} and A={1,4}, find A′−A.
If U={1,2,3,4,5,6} and A={1,2,3}, find A′.
If U={1,2,3,4,5,6} and A=U, find A′.
If A={m,n,o,p} and B={o,p,q,r}, find A−B.
If A={1,2,3} and B={2,3,4}, find B−A.
If U={a,b,c,d} and A={a,b}, find (A′)′.
If A={x,y,z} and B={y,z}, find B−A.
If U={1,2,3,4,5} and A=∅, find A′.
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