If $\mathrm{p}, \mathrm{q}$ are true statements and $\mathrm{r}$ is false statement, then which of the…
If $\mathrm{p}, \mathrm{q}$ are true statements and $\mathrm{r}$ is false statement, then which of the following is correct.
- $(p \vee q) \vee r$ has truth value $F$.
- $(p \wedge q) \rightarrow r$ has truth value $T$.
- $(\mathrm{p} \rightarrow \mathrm{r}) \rightarrow \mathrm{q}$ has truth value $\mathrm{F}$.
- $(\mathrm{p} \leftrightarrow \mathrm{q}) \rightarrow \mathrm{r}$ has truth value $F$.
Solution
We will go by option
(1) $(\mathrm{p} \vee \mathrm{q}) \vee \mathrm{r} \equiv(\mathrm{T} \vee \mathrm{T}) \vee \mathrm{F} \equiv \mathrm{T} \vee \mathrm{F} \equiv \mathrm{T}$
(2) $(\mathrm{p} \wedge \mathrm{q}) \rightarrow \mathrm{r} \equiv(\mathrm{T} \wedge \mathrm{T}) \rightarrow \mathrm{F} \equiv \mathrm{T} \rightarrow \mathrm{F} \equiv \mathrm{F}$
(3) $(\mathrm{p} \rightarrow \mathrm{r}) \rightarrow \mathrm{q} \equiv(\mathrm{T} \rightarrow \mathrm{F}) \rightarrow \mathrm{T} \equiv \mathrm{F} \rightarrow \mathrm{T} \equiv \mathrm{T}$
(4) $(\mathrm{p} \leftrightarrow \mathrm{q}) \rightarrow \mathrm{r} \equiv(\mathrm{T} \leftrightarrow \mathrm{T}) \rightarrow \mathrm{F} \equiv \mathrm{T} \rightarrow \mathrm{F} \equiv \mathrm{F}$
Asked in: MHT CET 2021 (21 Sep Shift 1)
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