Mastering Complements and Differences in Sets

  • 12th Grade
Reviewed by Cierra Henderson
Cierra Henderson, MBA |
K-12 Expert
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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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Quizzes Created: 8157 | Total Attempts: 9,569,759
| Attempts: 13 | Questions: 10 | Updated: Jan 21, 2026
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Question 1 / 11
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1) If U={1,2,3,4,5,6}, A={2,4,6}, find A′−A.

Explanation

A′ = {1,3,5}; removing A leaves same set.

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About This Quiz
Mastering Complements and Differences In Sets - Quiz

Ever wonder what’s outside a set or what’s left over when you subtract one set from another? Complements and differences are key tools in set theory that help describe exactly that. In this quiz, you’ll practice identifying complements, finding set differences, and applying these ideas to mathematical problems. Take this... see morequiz to sharpen your set theory skills and build confidence for higher-level math.
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2) If U={a,b,c,d,e}, A={b,c,d}, B={c,d,e}, find A′−B.

Explanation

A′ = {a,e}; subtracting B leaves {a}.

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3) If A={1,2,3,4}, B={2,4}, find (A−B)′ assuming U={1,2,3,4,5,6}.

Explanation

A−B = {1,3}. Complement in U = {2,4,5,6}.

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4) If U={1,2,3,4,5,6,7}, A={1,2,3}, B={3,4,5}, find (A′ − B′).

Explanation

A′={4,5,6,7}, B′={1,2,6,7}. Difference = {4,5}.

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5) If U={1,2,3,4,5}, A={1,2,3}, B={2,3}, find (A′ − B).

Explanation

A′={4,5}. Subtracting B leaves {4,5}.

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6) If U={a,b,c,d,e,f}, A={a,b}, B={b,c,d}, find (B′ − A′).

Explanation

B′={e,f,a}, A′={c,d,e,f}. Difference = {a}.

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7) If U={1,2,3,4,5}, A={2,3}, B={3,4}, find (A−B)′.

Explanation

A−B={2}. Complement in U={1,3,4,5}.

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

Explanation

A′={1,4,5,6}. Subtracting A leaves the same set.

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9) If U={1,2,3,4,5}, A={1,2}, B={2,3,4}, find (A−B)′.

Explanation

A−B={1}. Complement in U={2,3,4,5}.

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

Explanation

A′={1,3,5}. Subtracting gives {2,4}.

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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={1,2,3,4,5,6}, A={2,4,6}, find A′−A.
If U={a,b,c,d,e}, A={b,c,d}, B={c,d,e}, find A′−B.
If A={1,2,3,4}, B={2,4}, find (A−B)′ assuming...
If U={1,2,3,4,5,6,7}, A={1,2,3}, B={3,4,5}, find (A′ −...
If U={1,2,3,4,5}, A={1,2,3}, B={2,3}, find (A′ − B).
If U={a,b,c,d,e,f}, A={a,b}, B={b,c,d}, find (B′ −...
If U={1,2,3,4,5}, A={2,3}, B={3,4}, find (A−B)′.
If U={1,2,3,4,5,6}, A={2,3}, find (A′ − A).
If U={1,2,3,4,5}, A={1,2}, B={2,3,4}, find (A−B)′.
If U={1,2,3,4,5}, A={2,4}, find (A − A′).
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