If p, $q$ are true statement and $\mathrm{r}$ is false statement, then which of the following atements is a…

If p, $q$ are true statement and $\mathrm{r}$ is false statement, then which of the following atements is a true statement.
  1. $(p \wedge q) \rightarrow r$ is true
  2. $(p \rightarrow r) \rightarrow q$ is false
  3. $(p \vee q) \vee r$ is false
  4. $(p \leftrightarrow q) \leftrightarrow r$ is false.

Solution

$(\mathrm{A})$ We have $\mathrm{p} \equiv \mathrm{T}, \mathrm{q} \equiv \mathrm{T}$ and $\mathrm{r} \equiv \mathrm{F}$ We will check truth value of each option. (A) $(\mathrm{p} \leftrightarrow \mathrm{q}) \leftrightarrow \mathrm{r}$ $\equiv(T \leftrightarrow T) \leftrightarrow F \equiv T \leftrightarrow F \equiv F$ (B) $(p \vee q) \vee r$ $\equiv(T \vee T) \vee F \equiv T \vee F=T$ (C) $(p \wedge q) \rightarrow r$ $\equiv(\mathrm{T} \wedge \mathrm{T}) \rightarrow \mathrm{F} \equiv \mathrm{T} \rightarrow \mathrm{F} \equiv \mathrm{F}$ (D) $(\mathrm{p} \rightarrow \mathrm{r}) \rightarrow \mathrm{q}$ $\equiv(T \rightarrow F) \rightarrow T \equiv F \rightarrow T \equiv T$

Asked in: MHT CET 2020 (16 Oct Shift 2)

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