Identifying Unions and Intersections (Basic)

  • 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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| Attempts: 14 | Questions: 10 | Updated: Jan 20, 2026
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1) A = {1, 2, 3, 4}, B = {3, 4, 5, 6}. Find A ∪ B.

Explanation

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

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About This Quiz
Identifying Unions and Intersections (Basic) - Quiz

Sets can overlap or stay separate—but do you know how to tell the difference? In this quiz, you’ll practice identifying unions and intersections, building a clear understanding of how sets combine. Try this quiz to sharpen your foundational set skills.

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

Explanation

Intersection contains common elements → {b, c}.

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

Explanation

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

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

Explanation

A ∪ B = {2, 3, 5, 7} → n = 4.

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

Explanation

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

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

Explanation

The only element common to all sets is 3.

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

Explanation

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

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

Explanation

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

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

Explanation

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

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

Explanation

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

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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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A = {1, 2, 3, 4}, B = {3, 4, 5, 6}. Find A ∪ B.
A = {a, b, c}, B = {b, c, d}. Find A ∩ B.
U = {1, 2, 3, 4, 5, 6}, A = {2, 4, 6}. Find A′.
A = {2, 3, 5}, B = {3, 5, 7}. Find n(A ∪ B).
A = {x, y, z}, B = {y, z}, C = {z}. Find A ∩ (B ∪ C).
A = {1, 2, 3}, B = {3, 4}, C = {2, 3, 5}. Find A ∩ B ∩ C.
A = {1, 3, 5, 7}, B = {2, 3, 4, 7}. Find (A ∩ B) ∪ {10}.
A = {2, 4, 6, 8}, B = {4, 8, 12}. Find (A ∪ B) ∩ {8, 10, 12}.
U = {1, 2, 3, 4, 5}, A = {1, 2}, B = {2, 3}. Find (A′ ∪ B′)′.
A = {m, n, o}, B = {n, o, p}, C = {o, p, q}. Find (A ∩ B) ∪ (B...
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