Set Theory → Complements & Differences

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1) 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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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 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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3) 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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4) 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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5) 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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6) 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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7) 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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8) 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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9) If U={a,b,c,d} and A={a,b}, find (A′)′.

Explanation

Double complement gives back the original set.

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10) 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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If U={1,2,3,4,5,6} and A={1,2,3}, find A′.
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 A={x,y,z} and B={y,z}, find B−A.
If U={1,2,3,4,5} and A=∅, 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 U={1,2,3,4} and A={1,4}, find A′−A.
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