Set Theory Part 5 Quiz

Set Theory Part 5 Quiz brings you into the fascinating world of set operations where logic meets simplicity. Many people are surprised to learn that the language of sets was first formalized by Georg Cantor in the late nineteenth century. He faced strong resistance from other mathematicians who felt his ideas were too abstract, yet today his work forms the backbone of modern mathematics. Concepts like union and intersection help us organize information in the clearest possible way, while the complement of sets shows how missing elements can also tell a story. This quiz continues that tradition, offering thoughtful practice that strengthens your understanding of how sets behave and relate within a universal set.

Set Theory Part

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, then what does (A ∪ B) − (A ∩ B) equal to?

{1, 2, 5, 6}

{3, 4}

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

{ }

If U = {1, 2, 3, 4, 5, 6}, A = {1, 3, 5}, then what is (A′)′

{ }

{2, 4, 6}

If A − B = {2 ,4} and A ∩ B = {6}, which of the following can be A?

{2, 4, 6}

{2, 4}

{6}

{2, 4, 8}

If A ⊂ B and B ⊂ C, then which is always true?

A = C

C ⊂ A

A ∪ C = A

A ⊂ C

If A ∪ B = U and A ∩ B = { }, then what is A′ equal to?

{ }

B′

If A = {1, 2, 3}, B = {2, 3, 4}, then what is A ∩ B′ equal to?

{4}

{1}

{ }

{2}

Which of the following is always empty?

A ∪ A′

A ∩ A′

A − A′

A ∩ U

If A = {a, b, c}, B = {b, c, d}, then (A − B) ∪ (B − A) equals?

{b, c}

{a, b, c, d}

{ }

{a, d}

If A ⊂ U, then A ∪ A′ equals?

{ }

A′

If A − B = { }, then which must be true?

B ⊂ A

A ⊂ B

A = { }

A ∩ B = { }

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Sample Questions from This Quiz

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, then what does (A ∪ B) − (A ∩ B) equal to?
If U = {1, 2, 3, 4, 5, 6}, A = {1, 3, 5}, then what is (A′)′?
If A − B = {2 ,4} and A ∩ B = {6}, which of the following can be A?
If A ⊂ B and B ⊂ C, then which is always true?
If A ∪ B = U and A ∩ B = { }, then what is A′ equal to?

Try the full quiz and see how many of these you can answer!