Question

(ii) Simplify as far as possible the set Pn (Q-P)'​

Answer 1

$\textbf{Given:}$

$P{\cap}(Q-P)'$

$\textbf{To simplify:}$

$P{\cap}(Q-P)'$

$\textbf{Solution:}$

$\text{Consider,}$

$P{\cap}(Q-P)'$

$\text{Using,}\;\boxed{\bf\,A-B=A{\cap}B'}$

$=P{\cap}(Q{\cap}P\,')'$

$\text{Using,}\;\boxed{\bf\,(A{\cap}B)'=A'{\cup}B'}$

$=P{\cap}(Q\,'{\cup}(P\,')')$

$=P{\cap}(Q\,'{\cup}P)$

$=(P{\cap}Q\,'){\cup}(P{\cap}P)$

$=(P{\cap}Q\,'){\cup}P$

$=(P-Q){\cup}P$

$\text{We know that, \bf\,P-Q\,{\subset}\,P }$

$=P$

$\therefore\bf\,P{\cap}(Q-P)\,'=P$