## Images of intersections and unions

For the mapping $$f: A\to B$$ and $$M,M'\subseteq A;\ N,N'\subseteq B$$ replace $$\Box$$ with the appropriate relation $$\subseteq, =$$ or $$\supseteq$$. If equality does not apply, characterize the mappings for which equality holds.

• #### Variant 1

$$f(M\cup M')\ \Box\ f(M) \cup f(M')$$.

• #### Variant 2

$$f(M\cap M')\ \Box\ f(M) \cap f(M')$$.

• #### Variant 3

$$f(M\setminus M')\ \Box\ f(M) \setminus f(M')$$.

• #### Variant 4

$$f^{-1}(N\cup N')\ \Box\ f^{-1}(N) \cup f^{-1}(N')$$.

• #### Variant 5

$$f^{-1}(N\cap N')\ \Box\ f^{-1}(N) \cap f^{-1}(N')$$.

• #### Variant 6

$$f^{-1}(N\setminus N')\ \Box\ f^{-1}(N) \setminus f^{-1}(N')$$.