Let p, q, r be three statements such that the truth value

Question:

Let $\mathrm{p}, \mathrm{q}, \mathrm{r}$ be three statements such that the truth value of $(p \wedge q) \rightarrow(\sim q \vee r)$ is $F$. Then the truth values of $\mathrm{p}, \mathrm{q}, \mathrm{r}$ are respectively :

  1. $\mathrm{T}, \mathrm{F}, \mathrm{T}$

  2. $\mathrm{F}, \mathrm{T}, \mathrm{F}$

  3. $\mathrm{T}, \mathrm{T}, \mathrm{F}$

  4. $\mathrm{T}, \mathrm{T}, \mathrm{T}$


Correct Option: , 3

Solution:

$(\mathrm{p} \wedge \mathrm{q}) \rightarrow(\sim \mathrm{q} \vee \mathrm{r})=$ false

when $(p \wedge q)=T$

and $(\sim \mathrm{q} \vee \mathrm{r})=\mathrm{F}$

So $(p \wedge q)=T$ is possible when $p=q=$ true

$\therefore \quad \sim \mathrm{q}=$ False $(\mathrm{q}=$ true $)$

So $(\sim \mathrm{q} \vee \mathrm{r})=$ False is possible if $\mathrm{r}$ is false

$\therefore \mathrm{p}=\mathrm{T}, \mathrm{q}=\mathrm{T}, \mathrm{r}=\mathrm{F}$

 

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