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Mathematical Reasoning
hard
જો $\left( {p \wedge \sim q} \right) \wedge \left( {p \wedge r} \right) \to \sim p \vee q$ એ અસત્ય હોય તો $p, q$ અને $r$ ના સત્યાર્થતાનું મુલ્ય અનુક્રમે ...............થાય .
A
$F, T, F$
B
$T, F, T$
C
$F, F, F$
D
$T, T, T$
(JEE MAIN-2018)
Solution
AS the truth table for $\left( { \sim p \wedge \sim q} \right) \wedge \left( {p \wedge r} \right) \to \sim p \wedge q$ is false, then only possible values of $(p,q,r)$ is $(T,F,T,)$
| $p$ | $q$ | $r$ | ${ \sim q}$ | $p \wedge \sim q$ | $p \wedge r$ | $\sim p$ | $ \sim p \vee q$ | $\left( {p \wedge \sim q} \right) \wedge \left( {p \wedge r} \right)$ | $\left( {p \wedge \sim q} \right) \wedge \left( {p \wedge \sim r} \right) \to \sim p \vee q$ |
| $T$ | $T$ | $T$ | $F$ | $F$ | $T$ | $F$ | $T$ | $F$ | $T$ |
| $T$ | $F$ | $T$ | $T$ | $T$ | $T$ | $F$ | $F$ | $T$ | $F$ |
| $T$ | $T$ | $F$ | $F$ | $F$ | $F$ | $F$ | $T$ | $F$ | $T$ |
| $F$ | $T$ | $T$ | $F$ | $F$ | $F$ | $T$ | $T$ | $F$ | $T$ |
| $F$ | $F$ | $T$ | $T$ | $F$ | $F$ | $T$ | $T$ | $F$ | $T$ |
| $F$ | $T$ | $F$ | $F$ | $F$ | $F$ | $T$ | $T$ | $F$ | $T$ |
| $T$ | $F$ | $F$ | $T$ | $T$ | $F$ | $F$ | $F$ | $F$ | $T$ |
| $F$ | $F$ | $F$ | $T$ | $F$ | $F$ | $T$ | $T$ | $F$ | $T$ |
Standard 11
Mathematics
