Set Complements & Mixed Operations Quiz � Work with ?, ?, and complements (HSS.CP.A.1)

1) Given A = {p, q, r}, B = {q, r, s}, C = {r, s, t}, find A ∩ (B ∪ C).

{q, r}

{p, q}

{r, s}

{p, q, r, s}

B ∪ C = {q, r, s, t}; intersect with A = {q, r}.

Explanation

B ∪ C = {q, r, s, t}; intersect with A = {q, r}.

2) Given A = {1, 2, 3}, B = {2, 3, 4}, C = {3, 4, 5}, find A ∩ B ∩ C.

{3}

{2, 3}

{4}

{2, 3, 4}

The only element common to all three sets is 3.

Explanation

The only element common to all three sets is 3.

3) Given A = {x, y}, B = {y, z}, C = {z, x}, find A ∪ (B ∩ C).

{x, y, z}

{x, y}

{y, z}

{z}

B ∩ C = {z}; union with A = {x, y, z}.

Explanation

B ∩ C = {z}; union with A = {x, y, z}.

4) Given A = {1, 4, 7}, B = {2, 4, 6}, C = {4, 6, 8}, find (A ∪ B) ∩ C.

{4, 6}

{6, 8}

{4}

{2, 4, 6}

A ∪ B = {1, 2, 4, 6, 7}; intersect with C = {4, 6}.

Explanation

A ∪ B = {1, 2, 4, 6, 7}; intersect with C = {4, 6}.

5) Given A = {x, y, z}, B = {y, z}, C = {z}, find (A ∪ B)′ if U = {w, x, y, z}.

{w}

{x}

{y, z}

∅

A ∪ B = {x, y, z}; complement in U = {w}.

Explanation

A ∪ B = {x, y, z}; complement in U = {w}.

6) Given A = {1, 3, 5}, B = {2, 3, 4}, find A ∩ B′ if U = {1, 2, 3, 4, 5}.

{1, 5}

{2, 4}

{3}

{1, 2, 5}

B′ = {1, 5}; A ∩ B′ = {1, 5}.

Explanation

B′ = {1, 5}; A ∩ B′ = {1, 5}.

7) Given A = {2, 4, 6}, B = {4, 6, 8}, find (A ∪ B)′ if U = {2, 4, 6, 8, 10}.

{10}

{2}

{4, 6, 8}

{8, 10}

A ∪ B = {2, 4, 6, 8}; complement in U = {10}.

Explanation

A ∪ B = {2, 4, 6, 8}; complement in U = {10}.

8) Given A = {2, 4, 6}, B = {4, 5, 6}, find A ∪ (B ∩ A′).

{2, 4, 5, 6}

{2, 4, 6}

{4, 5, 6}

{2, 5, 6}

A′ relative to U (assumed superset) excludes A’s elements. B ∩ A′ = {5}. Union with A = {2, 4, 5, 6}.

Explanation

A′ relative to U (assumed superset) excludes A’s elements. B ∩ A′ = {5}. Union with A = {2, 4, 5, 6}.

9) Given A = {1, 2, 3}, B = {3, 4, 5}, find n(A ∩ B′) if U = {1, 2, 3, 4, 5}.

2

1

3

4

B′ = {1, 2}; A ∩ B′ = {1, 2}. So n = 2.

Explanation

B′ = {1, 2}; A ∩ B′ = {1, 2}. So n = 2.

10) Given A = {a, b}, B = {b, c}, find (A′ ∪ B)′ if U = {a, b, c, d}.

{a}

∅

{b}

{c, d}

A′ = {c, d}; A′ ∪ B = {b, c, d}; complement in U = {a}.

Explanation

A′ = {c, d}; A′ ∪ B = {b, c, d}; complement in U = {a}.

Set Theory → Union and Intersection