Let

$\displaystyle F:a\rightarrow b$

be a function

The image of $\displaystyle x\subseteq a$ through F is the set $\displaystyle F[x] =\{F(z): z \epsilon x\}$

The preimage of $\displaystyle y\subseteq b$ through F is the set $\displaystyle F^-^1 =\{z\epsilon a: F(z) \epsilon y\}$

Give a proof or a counterexample

a.If w is a nonempty set of subsets of a then $\displaystyle F[\bigcup w] = \bigcup \{F[x]:x\epsilon w\}$

b.If w is a nonempty set of subsets of a then $\displaystyle F[\bigcap w] = \bigcap \{F[x]:x\epsilon w\}$

c.If w is a nonempty set of subsets of b then $\displaystyle F^-^1[\bigcup w] = \bigcup \{F^-^1[x]:x\epsilon w\}$

d.If w is a nonempty set of subsets of b then $\displaystyle F^-^1[\bigcap w] = \bigcap \{F^-^1[x]:x\epsilon w\}$

I'm just having trouble seeing these so any help would be much appreciated