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# Image and Preimage of Subsets

TOPO-NJDGR4

$f:X\rightarrow Y$ is a map, $A$ is a subset of $X$.

Which of the following statements are always TRUE?

Select ALL that apply.

A

$f(A)\subseteq f(f^{-1}(f(A)))$

B

$f(f^{-1}(f(A)))\subseteq f(A)$

C

$A\subseteq f^{-1}(f(A))$

D

$f^{-1}(f(A))\subseteq A$

E

$f^{-1}(f(f^{-1}(f(A))))\subseteq f^{-1}(f(A))$

F

$f^{-1}(f(A))\subseteq f^{-1}(f(f^{-1}(f(A))))$