## 5 Answers

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.

Here it is given that

**a ↔(b v ¬b) ≡ a ↔ True**

so value of a will be true

Now **b ↔ c** means when b is true c will be true true or when b is false c will be false

case 1: Let's take b as TRUE

so, c will be TRUE

so, for expression **[(a∧b)→(a∧c)∨d ]**

a is true and b is true so a∧b true and a∧c true so both LHS and RHS are true hence the expression will be **true**

when b is false c is also false as LHS is false the expression will always be **true**

so answer is **(A) true**