show that fA subset of fB does not always mean A is a subset

show that f(A) subset of f(B) does not always mean A is a subset of B.

sol:

for example : let f(x)=x²

^{let A={1,2,3}}

^{let B={-1,-2,-3,-4}}

^{but A is not sub set of B}

^{and agian f(A)={1,4,,9,16}}

^{so f(A) subset of f(B)}

^{this is a counter example}