Question

If $P\left(A\right)$ denotes power set of set $A$, then

• A. $P\left(A\right)\cap \left\{A\right\}=\left\{A\right\}$
• B. $P\left(A\right)\cap \left\{A\right\}=\varphi$
• C. $P\left(A\right)\cap \left\{A\right\}=P\left(A\right)$
• D. $P\left(A\right)\cup \left\{A\right\}=P\left(A\right)$

Answer 1

Answer: (A), (D)

$P\left(A\right)\cap \left\{A\right\}=\left\{A\right\}$
$P\left(A\right)\cup \left\{A\right\}=P\left(A\right)$

Consider $A=\{a,b\}$ then $P\left(A\right)=\{\varphi ,\{a\},\{b\},\{a,b\left\}\right\}$
$\therefore P\left(A\right)\bigcap \left\{A\right\}=\{\varphi ,\{a\},\{b\},\{a,b\left\}\right\}\bigcap \left\{\right\{a,b\left\}\right\}=\left\{\right\{a,b\left\}\right\}=\left\{A\right\}$
$P\left(A\right)\bigcup \left\{A\right\}=\{\varphi ,\{a\},\{b\},\{a,b\left\}\right\}$