## Images of intersections and unions

### Task number: 2811

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

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