Option(B)
LHS= p$\leftrightarrow$q
= (~p V q) $\wedge$ (~q V p)
RHS=(p $\wedge$ q) V (~p $\wedge$ ~q)
= (p V (~p $\wedge$ ~q)) $\wedge$ (q V (~p $\wedge$ ~q))
= ((p V ~p) $\wedge$ (p V ~q)) $\wedge$ ((q V ~p) $\wedge$ (q V ~q)
= (p V ~q) $\wedge$ (q V ~p)
=LHS
Hence option (B) is true
Option (C)
LHS=~(p $\wedge$ ~q)
=(~p V q)
= p $\rightarrow$ q
RHS=(p $\rightarrow$ ~q)
$\neq$ LHS
Hence option (C) is not true