Identifying Unions and Intersections (Basic)

1) A = {1, 2, 3, 4}, B = {3, 4, 5, 6}. Find A ∪ B.

{1, 2, 3, 4, 5, 6}

{1, 2, 3, 4}

{3, 4, 5, 6}

{1, 2, 5, 6}

Union combines all unique elements from A and B → {1, 2, 3, 4, 5, 6}.

Explanation

Union combines all unique elements from A and B → {1, 2, 3, 4, 5, 6}.

2) A = {a, b, c}, B = {b, c, d}. Find A ∩ B.

{b, c}

{a, b, c, d}

{a, d}

{c, d}

Intersection contains common elements → {b, c}.

Explanation

Intersection contains common elements → {b, c}.

3) U = {1, 2, 3, 4, 5, 6}, A = {2, 4, 6}. Find A′.

{1, 3, 5}

{2, 4, 6}

{1, 2, 3}

{3, 5, 6}

Complement = all elements in U not in A → {1, 3, 5}.

Explanation

Complement = all elements in U not in A → {1, 3, 5}.

4) A = {2, 3, 5}, B = {3, 5, 7}. Find n(A ∪ B).

4

3

5

6

A ∪ B = {2, 3, 5, 7} → n = 4.

Explanation

A ∪ B = {2, 3, 5, 7} → n = 4.

5) A = {1, 3, 5, 7}, B = {2, 3, 4, 7}. Find (A ∩ B) ∪ {10}.

{3, 7, 10}

{3, 7}

{1, 2, 3, 4, 5, 7, 10}

{7, 10}

A ∩ B = {3, 7}; adding {10} → {3, 7, 10}.

Explanation

A ∩ B = {3, 7}; adding {10} → {3, 7, 10}.

6) A = {x, y, z}, B = {y, z}, C = {z}. Find A ∩ (B ∪ C).

{y, z}

{x, y, z}

{z}

{x, y}

B ∪ C = {y, z}; intersect with A = {y, z}.

Explanation

B ∪ C = {y, z}; intersect with A = {y, z}.

7) A = {1, 2, 3}, B = {3, 4}, C = {2, 3, 5}. Find A ∩ B ∩ C.

{3}

{2, 3}

{2}

{4}

The only element common to all sets is 3.

Explanation

The only element common to all sets is 3.

8) A = {2, 4, 6, 8}, B = {4, 8, 12}. Find (A ∪ B) ∩ {8, 10, 12}.

{8, 12}

{4, 8, 12}

{8}

{10}

A ∪ B = {2, 4, 6, 8, 12}; intersect with {8, 10, 12} = {8, 12}.

Explanation

A ∪ B = {2, 4, 6, 8, 12}; intersect with {8, 10, 12} = {8, 12}.

9) U = {1, 2, 3, 4, 5}, A = {1, 2}, B = {2, 3}. Find (A′ ∪ B′)′.

{2}

{1, 3}

{4, 5}

{2, 3}

A′ = {3, 4, 5}, B′ = {1, 4, 5}; union = {1, 3, 4, 5}. Complement = {2}.

Explanation

A′ = {3, 4, 5}, B′ = {1, 4, 5}; union = {1, 3, 4, 5}. Complement = {2}.

10) A = {m, n, o}, B = {n, o, p}, C = {o, p, q}. Find (A ∩ B) ∪ (B ∩ C).

{n, o, p}

{o, p}

{n, o}

{m, n, o, p, q}

A ∩ B = {n, o}, B ∩ C = {o, p}. Union = {n, o, p}.

Explanation

A ∩ B = {n, o}, B ∩ C = {o, p}. Union = {n, o, p}.