MHT CET · Maths · Mathematical Reasoning
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?
- A \((p \wedge q) \rightarrow r\) has truth value False.
- B \((\mathrm{p} \rightarrow \mathrm{q}) \rightarrow \mathrm{r}\) has truth value True.
- C \((p \vee q) \leftrightarrow r\) has truth value False.
- D \((\mathrm{p} \rightarrow \mathrm{q}) \rightarrow(\mathrm{q} \rightarrow \mathrm{p})\) has truth value True.
Answer & Solution
Correct Answer
(C) \((p \vee q) \leftrightarrow r\) has truth value False.
Step-by-step Solution
Detailed explanation
The truth values of \(\mathrm{p}, \mathrm{q}\) and r are \(\mathrm{F}, \mathrm{T}\) and F respectively.
Consider option (C)
\(\begin{aligned}
& (p \vee q) \leftrightarrow r \\
& \equiv(F \vee T) \leftrightarrow F \\
& \equiv T \leftrightarrow F \\
& \equiv F .
\end{aligned}\)
Consider option (C)
\(\begin{aligned}
& (p \vee q) \leftrightarrow r \\
& \equiv(F \vee T) \leftrightarrow F \\
& \equiv T \leftrightarrow F \\
& \equiv F .
\end{aligned}\)
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