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Let f : X → Y and suppose that {Ai}i∈I is an indexed collection of subsets...

Let f : X → Y and suppose that {Ai}i∈I is an indexed collection of subsets of X. Show that f[∩i∈IAi ] ⊆ ∩i∈I f[Ai ]. Give an example, using two sets A1 and A2, to show that it’s possible for the LHS to be empty while the RHS is non-empty.

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