Question

Prove that if a is subset of phi then a = phi

$\mathit{Q}\mathbf{.}ProvethatifA\subset \varphi ,thenA=\varphi .$

Answer 1

Dear student
$$\begin{gathered} \mathrm{We}\mathrm{know}\mathrm{that}\mathrm{two}\mathrm{sets}\mathrm{A}\mathrm{and}\mathrm{B}\mathrm{are}\mathrm{equal}\mathrm{iff}\mathrm{A}\subset \mathrm{B}\mathrm{and}\mathrm{B}\subset \mathrm{A}.\mathrm{Also}\mathrm{we}\mathrm{know}\mathrm{that} \\ \mathrm{\varphi }\subset \mathrm{A} \\ \mathrm{and}\mathrm{A}\subset \mathrm{\varphi }\left[\mathrm{Given}\right] \\ \mathrm{So},\boxed{\mathbf{A}\mathbf{=}\mathbf{\varphi }} \end{gathered}$$
Regards