Question

Let X be a set, and \[f:X->X\]is a representation. Where\[A \subseteq X\]Now I need to prove or disprove that\[f(f^{-1}(A))\subseteq A\]

Answer 1

Let X be a set, and \[f:X->X\]is a representation. Where\[A \subseteq X\]Now I need to prove or disprove that\[f(f^{-1}(A))\subseteq A\]

Answer 2

there are no conditions such as f has to be one to one or bijective?

Answer 3

No, that is all I know

Answer 4

and \( f^{-1} (A) \) is the pre-image of \( A \)

Answer 5

if f is one to one , then it is true
because f( f^-1(A)) = A and A is a subset of A

Answer 6

what if f is not one to one

Answer 7

What does it mean that f is one to one?

Answer 8

distinct values in the domain map to distinct values in the co-domain