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Given that $\ a\Leftrightarrow (b\vee \sim b)$ and $ b\Leftrightarrow c$

Now,

$(a\wedge b)\rightarrow (a \wedge c)\vee d$

$\equiv (a\wedge b)\rightarrow (a \wedge b)\vee d$

$(\because b \Leftrightarrow c)$

$\equiv \neg (a\wedge b)\vee (a \wedge b)\vee d$

$\equiv T \vee d$

$\equiv T$

Hence, Option(**A**) True.