Let f: X→Y be a map with A1, A2⊂X andB1,B2⊂Y
(A) Provef(A1∪A2)=f(A1)∪f(A2).
(B) Provef(A1∩A2)⊂f(A1)∩f(A2).Give an example in which equality fails.
(C) Provef−1(B1∪B2)=f−1(B1)∪f−1(B2),where f−1(B)={x∈X: f(x)∈B}.
(D) Provef−1(B1∩B2)=f−1(B1)∩f−1(B2).
(E) Provef−1(Y∖B1)=X∖f−1(B1).
(Abstract Algebra)
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