If $\mathrm{p}$ and $\mathrm{q}$ are true statements and $\mathrm{r}$ and $s$ are false statements, then the…

If $\mathrm{p}$ and $\mathrm{q}$ are true statements and $\mathrm{r}$ and $s$ are false statements, then the truth values of the statement patterns $(p \wedge q) \vee r$ and $(\mathrm{p} \vee \mathrm{s}) \leftrightarrow(\mathrm{q} \wedge \mathrm{r})$ are respectively
  1. $\mathrm{F}, \mathrm{T}$
  2. $\mathrm{T}, \mathrm{T}$
  3. $\mathrm{F}, \mathrm{F}$
  4. $\mathrm{T}, \mathrm{F}$

Solution

$\begin{array}{ll}(\mathrm{p} \wedge \mathrm{q}) \vee \mathrm{r} & (\mathrm{p} \vee \mathrm{s}) \leftrightarrow(\mathrm{q} \wedge \mathrm{r}) \\ \equiv(T \wedge \mathrm{T}) \vee \mathrm{F} & \equiv(\mathrm{T} \vee \mathrm{F}) \leftrightarrow(\mathrm{T} \wedge \mathrm{F}) \\ \equiv \mathrm{T} \vee \mathrm{F} & \equiv \mathrm{T} \leftrightarrow \mathrm{F} \\ \equiv \mathrm{T} & \equiv \mathrm{F}\end{array}$

Asked in: MHT CET 2023 (10 May Shift 2)

Practice more Mathematical Logic questions on Aicharya