If p : The total prime numbers between 2 to 100 are 26 . q : Zero is a complex number. r : Least common…

If p : The total prime numbers between 2 to 100 are 26 . q : Zero is a complex number. r : Least common multiple (L.C.M.) of 6 and 7 is 6 . Then which of the following is correct?
  1. $(p \wedge q) \rightarrow r$ has truth value False.
  2. $(\mathrm{p} \rightarrow \mathrm{q}) \rightarrow \mathrm{r}$ has truth value True.
  3. $(p \vee q) \leftrightarrow r$ has truth value False.
  4. $(\mathrm{p} \rightarrow \mathrm{q}) \rightarrow(\mathrm{q} \rightarrow \mathrm{p})$ has truth value True.

Solution

The truth values of $\mathrm{p}, \mathrm{q}$ and r are $\mathrm{F}, \mathrm{T}$ and F respectively. Consider option (C) $\begin{aligned} & (p \vee q) \leftrightarrow r \\ & \equiv(F \vee T) \leftrightarrow F \\ & \equiv T \leftrightarrow F \\ & \equiv F . \end{aligned}$

Asked in: MHT CET 2024 (15 May Shift 2)

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