The statement p∧q⇒p∧r is equivalent to

Correct answer: (D) p∧q⇒r. Given, p∧q⇒p∧r {Using A⇒B≡~A∨B} =~p∧q∨p∧r {Using Demorgan's law ~A∧B≡~A∨~B} =~p∨~q∨p∧r =~p∨p∧r∨~q =~p∨p∧~p∨r∨~q =~p∨r∨~q =~p∨~q∨r =~p∧q∨r =p∧q⇒r

Q42 / 90 · JEE Main 2022 (29 Jul Shift 1) · Mathematics

The statement $(p \land q) \Rightarrow (p \land r)$ is equivalent to

A
$q \Rightarrow (p \land r)$
B
$p \Rightarrow (p \land r)$
C
$(p \land r) \Rightarrow (p \land q)$
Correct answer
D
$(p \land q) \Rightarrow r$

Solution

Given,
$(p \land q) \Rightarrow (p \land r)$
{Using $A \Rightarrow B \equiv ~ A \lor B$ }
$= ~ (p \land q) \lor (p \land r)$
{Using Demorgan's law $~ (A \land B) \equiv ~ A \lor ~ B$ }
$= (~ p \lor ~ q) \lor (p \land r)$
$= (~ p \lor (p \land r)) \lor ~ q$
$= (~ p \lor p) \land (~ p \lor r) \lor ~ q$
$= (~ p \lor r) \lor ~ q$
$= (~ p \lor ~ q) \lor r$
$= ~ (p \land q) \lor r$
$= (p \land q) \Rightarrow r$

Hence, the correct answer is option: 'D'.

The statement p∧q⇒p∧r is equivalent to

Solution

Relevant Questions

The statement $(p \land q) \Rightarrow (p \land r)$ is equivalent to