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Functions

Let f : X → Y be a function from the set X to the set Y , and let A, B be subsetsof X and C, D subsets of Y . Show that:
a)) if f is injective, then f(A ∩ B) = f(A) ∩ f(B)
b) f−1(C ∪ D) = f−1(C) ∪ f−1(D)

Please help :frown:
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Zacken
22
Original post by Lunu
Let f : X → Y be a function from the set X to the set Y , and let A, B be subsetsof X and C, D subsets of Y . Show that:
a)) if f is injective, then f(A ∩ B) = f(A) ∩ f(B)
b) f−1(C ∪ D) = f−1(C) ∪ f−1(D)

Please help :frown:


As for the first part, what does it mean for a function to be injective? Work from the definition.

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