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Let f: X→Y be a map with A1, A2⊂X and B1,B2⊂Y (A) Prove f(A1∪A2)=f(A1)∪f(A2). (B) Prove f(A1∩A2)⊂f(A1)∩f(A2). Give an example in...

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Advance Math

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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