Tuesday, October 4, 2016

functions - Show f1(Ac)=(f1(A))c


Let f:XY, and AY. Show that f1(Ac)=(f1(A))c


I know how to prove that f1(Ac)(f1(A))c, but stuck on proving (f1(A))cf1(Ac). Could someone help with this step please? Thanks.


Answer



Suppose x(f1(A))c. Then xX and xf1(A). Thus f(x)A, and of course f(x)Y, so f(x)Ac. Therefore xf1(Ac).


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