Question

If $A=\{\left\{2\right\},\left\{\varphi \right\},\varphi \}$ then $P\left(A\right)$ is

• A. $\{\left\{2\right\},\left\{\varphi \right\},\left\{\left\{\varphi \right\}\right\}\}$
• B. $\{\varphi ,\left\{2\right\},\left\{\varphi \right\},\{\varphi ,\left\{2\right\}\}\},\{\left\{\varphi \right\},\left\{2\right\}\},\{\left\{\varphi \right\},\varphi \},\{\left\{\varphi \right\},\left\{2\right\},\left\{\varphi \right\},\left\{\left\{\varphi \right\}\right\}\}$
• C. $\{\{2,\varphi \},\varphi ,\left\{\varphi \right\},\left\{2\right\},\{\varphi ,\left\{2\right\}\}\}$
• D. None of these

Answer 1

Answer: (B)

$\{\varphi ,\left\{2\right\},\left\{\varphi \right\},\{\varphi ,\left\{2\right\}\}\},\{\left\{\varphi \right\},\left\{2\right\}\},\{\left\{\varphi \right\},\varphi \},\{\left\{\varphi \right\},\left\{2\right\},\left\{\varphi \right\},\left\{\left\{\varphi \right\}\right\}\}$

Set $A=\{\left\{2\right\},\left\{\varphi \right\},\varphi \}$

then Power set $P\left(A\right)$

$=\{\varphi ,\left\{2\right\},\left\{\varphi \right\},\{\varphi ,\left\{2\right\}\}\},\{\left\{\varphi \right\},\left\{2\right\}\},\{\left\{\varphi \right\},\varphi \},\{\left\{\varphi \right\},\left\{2\right\},\left\{\varphi \right\},\left\{\left\{\varphi \right\}\right\}\}$