Consider the following two propositions : P_1: ~p→~q P_2: p∧~q∧~p∨q If the proposition p→~p∨q is evaluated as FALSE, then

Correct answer: (C) Both P_1 and P_2 are FALSE. p q ~p ~q ~p∨q p→~p∨q p→~q ~p→~q p∧~q p∧~q∧~p∨q T T F F T T F T F F T F F T F F T F T F F T T F T T T F F F F F T T T T T F F F p→~p∨q is F when p is true q is false from the table. Hence, P_1 & P_2 both are false

Q36 / 90 · JEE Main 2022 (25 Jun Shift 1) · Mathematics

Consider the following two propositions :
$P_{1}$ : $~ (p \to ~ q)$
$P_{2}$ : $(p \land ~ q) \land ((~ p) \lor q)$
If the proposition $p \to ((~ p) \lor q)$ is evaluated as FALSE, then

A
$P_{1}$ is TRUE and $P_{2}$ is FALSE
B
$P_{1}$ is FALSE and $P_{2}$ is TRUE
Correct answer
C
Both $P_{1}$ and $P_{2}$ are FALSE
D
Both $P_{1}$ and $P_{2}$ are TRUE

Solution

$p$	$q$	$~ p$	$~ q$	$~ p \lor q$	$p \to (~ p \lor q)$	$p \to ~ q$	$~ (p \to ~ q)$	$p \land ~ q$	$(p \land ~ q) \land ((~ p) \lor q)$
$T$	$T$	$F$	$F$	$T$	$T$	$F$	$T$	$F$	$F$
$T$	$F$	$F$	$T$	$F$	$F$	$T$	$F$	$T$	$F$
$F$	$T$	$T$	$F$	$T$	$T$	$T$	$F$	$F$	$F$
$F$	$F$	$T$	$T$	$T$	$T$	$T$	$F$	$F$	$F$

$p \to (~ p \lor q)$ is $F$ when $p$ is true $q$ is false from the table.

Hence, $P_{1} & P_{2}$ both are false

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

Consider the following two propositions :P1: ~p→~qP2: p∧~q∧~p∨qIf the proposition p→~p∨q is evaluated as FALSE, then

Solution

Relevant Questions

Consider the following two propositions :
$P_{1}$ : $~ (p \to ~ q)$
$P_{2}$ : $(p \land ~ q) \land ((~ p) \lor q)$
If the proposition $p \to ((~ p) \lor q)$ is evaluated as FALSE, then