Задача 6.

Consider $f\colon X\rightarrow Y$, $A_1, A_2\subset X$, $B_1, B_2\subset Y$. Is the following always true? a) $f[X]=Y$; b) $f^{-1}[Y]=X$; c) $f[A_1\cup A_2]=f[A_1]\cup f[A_2]$; d) $f[A_1\cap A_2] = f[A_1]\cap f[A_2]$; e) $f^{-1}[B_1\cup B_2] = f^{-1}[B_1]\cup f^{-1}[B_2]$; f) $f^{-1}[B_1\cap B_2] = f^{-1}[B_1]\cap f^{-1}[B_2]$; g) $f[A_1]\subset f[A_2] \Rightarrow A_1\subset A_2$; h) $f^{-1} [B_1] \subset f^{-1}[B_2]\Rightarrow B_1\subset B_2$.