JEE Main 2022 · 25 Jun · Shift 1 · Mathematics Q7

MathematicsSingle correct+4 / -1Question 7 of 90

Consider the following two propositions :

P1 : $\sim(p\rightarrow\sim q)$

P2 : $(p\wedge\sim q)\wedge((\sim p)\vee q)$

If the proposition $p\rightarrow((\sim p)\vee q)$ is evaluated as FALSE, then :

P1 is TRUE and P2 is FALSE

P1 is FALSE and P2 is TRUE

Both P1 and P2 are FALSE

Both P1 and P2 are TRUE

Answer and worked solution

Official answer: C

When is it false? $p\rightarrow((\sim p)\vee q)$ is false only if $p$ is T and $(\sim p)\vee q$ is F, so $q$ is F.

P1. $\sim(p\rightarrow\sim q)\equiv p\wedge q=$ F.

P2. $(p\wedge\sim q)=$ T but $(\sim p)\vee q=$ F, so P2 is F.

Both false.

(C)

Topics:Mathematical reasoning

JEE Main 2022 · 25 Jun · Shift 1, Mathematics question 7