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QJEEM23Maf942: JEE Main 2023 Mathematics - Class 11 JEEM23Maf942 Solution: The number of ordered triplets of the truth values of and such…

The number of ordered triplets of the truth values of p,qp, q and rr such that the truth value of the statement (p∨q)∧(p∨r)⇒(q∨r)(p \vee q) \wedge(p \vee r) \Rightarrow(q \vee r) is True, is equal to ___________.

Step-by-Step Verified Solution

pamp;qamp;ramp;p∨qamp;p∨ramp;(p∨q)∧(p∨r)amp;q∨ramp;(p∨q)∧(p∨r)⇒(q∨r)Tamp;Tamp;Tamp;Tamp;Tamp;Tamp;Tamp;TTamp;Tamp;Famp;Tamp;Tamp;Tamp;Tamp;TTamp;Famp;Tamp;Tamp;Tamp;Tamp;Tamp;TTamp;Famp;Famp;Tamp;Tamp;Tamp;Famp;FFamp;Tamp;Tamp;Tamp;Tamp;Tamp;Tamp;TFamp;Tamp;Famp;Tamp;Famp;Famp;Tamp;TFamp;Famp;Tamp;Famp;Tamp;Famp;Tamp;TFamp;Famp;Famp;Famp;Famp;Famp;Famp;T\begin{array}{|c|c|c|c|c|c|c|c|} \hline \boldsymbol{p} & \boldsymbol{q} & \boldsymbol{r} & \boldsymbol{p} \vee \boldsymbol{q} & \boldsymbol{p} \vee \boldsymbol{r} & \begin{array}{c} (\boldsymbol{p} \vee \boldsymbol{q}) \wedge \\ (\boldsymbol{p} \vee \boldsymbol{r}) \end{array} & \boldsymbol{q} \vee \boldsymbol{r} & \begin{array}{c} (\boldsymbol{p} \vee \boldsymbol{q}) \wedge(\boldsymbol{p} \vee \boldsymbol{r}) \\ \Rightarrow(\boldsymbol{q} \vee \boldsymbol{r}) \end{array} \\ \hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} \\ \hline \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T} \\ \hline \end{array}

Hence, the total number of ordered triplets are 7.

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