1. Tardigrade
  2. Question
  3. Mathematics
  4. If (p ∧ ∼ q) ∧ (p ∧ r) → ∼ p ∨ q is false, then the truth values of p, q and r are, respectively :

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If $(p \, \wedge \, \sim q) \wedge (p \wedge \, r) \to \sim p \vee q$ is false, then the truth values of p, q and r are, respectively :

JEE MainJEE Main 2018Mathematical Reasoning

Solution:

$\left(p\wedge \sim q\right)\wedge\left(p\wedge\sim r\right)\to\sim p \vee q$
$\left(1\right)\quad\left(T\wedge F\right)\wedge\left(T\wedge T\right)\to\left(F\vee T\right)$
$\equiv\left(F\wedge T\right)\to T$
$\equiv F\to T\equiv T$
$\left(2\right)\quad\left(F\wedge F\right)\wedge\left(F\wedge F\right)\to T \vee T$
$F \to T \equiv T$
$\left(3\right)\quad\left(T\wedge T\right)\wedge\left(T\wedge T\right)\to F \vee F$
$T\to F\equiv F$
$\left(4\right)\quad\left(F\wedge T\right)\wedge\left(F\wedge F\right)\to T \vee F$
$F\wedge F\to T$
$F\to T\equiv T$