Let 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.