A, B and C be sets. (a) Suppose that A ⊆ B and B ⊆ C....

A, B and C be sets.

(a) Suppose that A ⊆ B and B ⊆ C. Does this mean that A ⊆ C? Prove your answer. Hint: to prove that A ⊆ C you must prove the implication, “for all x, if x ∈ A then x ∈ C.”

(b) Suppose that A ∈ B and B ∈ C. Does this mean that A ∈ C? Give an example to prove that this does NOT always happen (and explain why your example works). You should be able to give an example where |A| = |B| = |C| = 2.

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Colby Messinger answered 1 year ago

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