$Given \ that \ a\Leftrightarrow (b\vee \sim b) \ and \ b\Leftrightarrow c$
$Now,$
$(a\wedge b)\rightarrow (a \wedge c)\vee d$
$\equiv (a\wedge b)\rightarrow (a \wedge b)\vee d$
$\equiv \sim (a\wedge b)\vee (a \wedge b)\vee d$
$\equiv T \vee d$
$\equiv T$
Hence,Option(A)True.