Question

If P c M, then which of the following set represent Pn(PuM)​

Answer 1

$\textbf{Given:}$

$P\,{\subset}\,M$

$\textbf{To find:}$

$P\,{\cap}(P{\cup}M)$

$\textbf{Solution:}$

$\text{We know that,}$

$\bf\,A,B\;\textbf{and}\;C\;\textbf{are any three sets}$

$\textbf{Then,}$

$\bf(i)\,A{\cap}(B{\cup}C)=(A{\cap}B){\cup}(A{\cap}C)$

$\bf(ii)\textbf{If \bf\,A\,{\subset}\,B, then \bf\,A{\cap}B=A }$

$\bf(iii)\textbf{For any set \bf\,A,\;\; \bf\,A{\cap}A=A }$

$\text{Consider,}$

$P\,{\cap}\,(P\,{\cup}\,M)$

$=(P\,{\cap}\,P)\,{\cup}\,(P\,{\cap}\,M)$

$=P{\cup}P$

$=P$

$\textbf{Answer:}$

$\boxed{\bf\,P\,{\cap}(P{\cup}M)=P}$

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

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Answer 2

Step-by-step explanation:

Given:

P\,{\subset}\,MP⊂M

\textbf{To find:}To find:

P\,{\cap}(P{\cup}M)P∩(P∪M)

\textbf{Solution:}Solution:

\text{We know that,}We know that,

\bf\,A,B\;\textbf{and}\;C\;\textbf{are any three sets}A,BandCare any three sets

\textbf{Then,}Then,

\bf(i)\,A{\cap}(B{\cup}C)=(A{\cap}B){\cup}(A{\cap}C)(i)A∩(B∪C)=(A∩B)∪(A∩C)

\bf(ii)\textbf{If $\bf\,A\,{\subset}\,B,$ then $\bf\,A{\cap}B=A$}(ii)If A⊂B, then A∩B=A

\bf(iii)\textbf{For any set $\bf\,A,\;\;$$\bf\,A{\cap}A=A$}(iii)For any set A,A∩A=A

\text{Consider,}Consider,

P\,{\cap}\,(P\,{\cup}\,M)P∩(P∪M)

=(P\,{\cap}\,P)\,{\cup}\,(P\,{\cap}\,M)=(P∩P)∪(P∩M)

=P{\cup}P=P∪P

=P=P

\textbf{Answer:}Answer:

\boxed{\bf\,P\,{\cap}(P{\cup}M)=P}

P∩(P∪M)=P

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