Given A and B are both subsets of X. Prove f : X ? Y is injective iff f(A ? B) =
ID: 1943149 • Letter: G
Question
Given A and B are both subsets of X. Prove f : X ? Y is injective iff f(A ? B) = f(A) ? f(B).Explanation / Answer
f:X->Y injctive means there is one one correspondence between X and Y elements. if we take f(AnB) then it will map AnB to some Y followed by one one correspondence.So if a belongs to A and also belongs to B then a should have only 1 element in Y but that does not satisfy the condition of injction that is every element should have only one element in Y.. .asso thatimplie A and B are disjoint set ,so f(AnB)=f(A)nf(B)
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