## If x is a subset of Y then, is inverse of x also a subset of Y?

Let $f : X \rightarrow Y$ be a function. If B is subset of y then its inverse image $f^-B$ is the subset of x define by $f^-B = {x : f(x) \in B}$ Now prove the following. $i. B_1 \subset B_2 \Rightarrow f^-B_1 \subset f^- B_1$ […]

## If x belongs to the domain then does f(x) belong to the range?

Let $F : x \Rightarrow y$ be a function. Then prove that $i. A_1 \subset A_2 \Rightarrow F(A_1) \subset F(A_2)$ $ii. F(\cup_i A_i) = \cup_i F(A_i)$ $iii.F(\cap_i A_i) \subset \cap_i f(A_i)$ Solution $Let \ f: x \rightarrow y$ be a function. i. $Let\ y \in f(A_1)$ \$Then\ \exists x \in […]

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