The compound statement P∨Q∧~P⇒Q equivalent to:

Correct answer: (D) ~P⇒Q⇔P∧~Q. P Q P∨Q ~P P∨Q∧~P P∨Q∧~P⇒Q T T T F F T T F T F F T F T T T T T F F F T F T P Q ~Q P∧~Q P⇒Q ~P⇒Q T T F F T F T F T T F T F T F F T F F F T F T F ~P⇒Q P∧~Q ~P⇒Q⇔P∧~Q F F T T T T F F T F F T Hence, P∨Q∧~P⇒Q equivalent to ~P⇒Q⇔P∧~Q

Q38 / 90 · JEE Main 2021 (27 Jul Shift 1) · Mathematics

The compound statement $(P \lor Q) \land (~ P) \Rightarrow Q$ equivalent to:

A
$P \lor Q$
B
$P \land ~ Q$
C
$~ (P \Rightarrow Q)$
Correct answer
D
$~ (P \Rightarrow Q) \Leftrightarrow P \land ~ Q$

Solution

$P$	$Q$	$P \lor Q$	$~ P$	$(P \lor Q) \land ~ P$	$(P \lor Q) \land ~ P \Rightarrow Q$
$T$	$T$	$T$	$F$	$F$	$T$
$T$	$F$	$T$	$F$	$F$	$T$
$F$	$T$	$T$	$T$	$T$	$T$
$F$	$F$	$F$	$T$	$F$	$T$

$P$	$Q$	$~ Q$	$P \land ~ Q$	$P \Rightarrow Q$	$~ (P \Rightarrow Q)$
$T$	$T$	$F$	$F$	$T$	$F$
$T$	$F$	$T$	$T$	$F$	$T$
$F$	$T$	$F$	$F$	$T$	$F$
$F$	$F$	$T$	$F$	$T$	$F$

$~ (P \Rightarrow Q)$	$P \land ~ Q$	$~ (P \Rightarrow Q) \Leftrightarrow P \land ~ Q$
$F$	$F$	$T$
$T$	$T$	$T$
$F$	$F$	$T$
$F$	$F$	$T$

Hence, $(P \lor Q) \land (~ P) \Rightarrow Q$ equivalent to $~ (P \Rightarrow Q) \Leftrightarrow P \land ~ Q$

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

The compound statement P∨Q∧~P⇒Q equivalent to:

Solution

Relevant Questions

The compound statement $(P \lor Q) \land (~ P) \Rightarrow Q$ equivalent to: