Question

For any two sets of A and B, prove that
$B^{\prime }\subset A^{\prime }\Rightarrow A\subset B$

Answer 1

To proof:-$A\subset Bif{B}^{{}^{\prime }}\subset A^{{}^{\prime }}$

Let $xϵA,sox\notin A^{{}^{\prime }}$ (by complement of set)

$\because B^{{}^{\prime }}\subset A^{{}^{\prime }}\&x\notin A^{{}^{\prime }}\therefore x\notin B^{{}^{\prime }}$

$So,xϵB\because for,xϵAwehave,xϵB\therefore A\subset B$