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Mathematical Reasoning
hard
જો $p \to ( \sim p\,\, \vee \, \sim q)$ અસત્ય હોય તો $p$ અને $q$ અનુક્રમે .............. થાય .
A
$T, F$
B
$F, F$
C
$F, T$
D
$T, T$
(JEE MAIN-2018)
Solution
| $p$ | $q$ | ${ \sim p}$ | ${ \sim q}$ | ${ \sim p \vee \sim q}$ | $p \to \left( { \sim p \vee \sim q} \right)$ |
| $T$ | $T$ | $F$ | $F$ | $F$ | $F$ |
| $T$ | $F$ | $F$ | $T$ | $T$ | $T$ |
| $F$ | $T$ | $T$ | $F$ | $T$ | $T$ |
| $F$ | $F$ | $T$ | $T$ | $T$ | $T$ |
Form the truth table,
$p \to \left( { \sim p \vee \sim q} \right)$ is false only when $p$ and $q$ both are true.
Standard 11
Mathematics
