Question

Доказать тождество.

Answer 1

$A\backslash(A\cap B )=\{x|(x\in A)\bigwedge (x\notin (A\cap B ))\}=\{x|(x\in A)\bigwedge (x\in (\overline{A}\cup \overline{B}) )\}=\{x|(x\in A)\bigwedge ((x\in \overline{A}) \bigvee (x\in \overline{B}) )\}=\{x|(x\in \o)\bigvee ((x\in A) \bigwedge (x\in \overline{B}) )\}=\{x|(x\in A) \bigwedge (x\in \overline{B}) \}=A\backslash B$