MHT CET · Maths · Mathematical Reasoning
Then symbolic from of the statement "If it does not rain today or I won't go to school, then I will meet my friend and I will go to watch a movie" is
p: It rains today
q: I am going to school
r: I will meet my friend
s: I will go to watch a movie
- A \(\sim(\mathrm{p} \vee \mathrm{q}) \rightarrow(\mathrm{r} \vee \mathrm{s})\)
- B \((p \wedge q) \rightarrow(r \vee s)\)
- C \(\sim(\mathrm{p} \wedge \mathrm{q}) \rightarrow(\mathrm{r} \wedge \mathrm{s})\)
- D \((\sim \mathrm{p} \wedge \mathrm{q}) \rightarrow(\mathrm{r} \wedge \mathrm{s})\)
Answer & Solution
Correct Answer
(C) \(\sim(\mathrm{p} \wedge \mathrm{q}) \rightarrow(\mathrm{r} \wedge \mathrm{s})\)
Step-by-step Solution
Detailed explanation
From the data given, symbolic form of the given statement is
\(
\begin{aligned}
& (\sim \mathrm{p} \vee \sim \mathrm{q}) \rightarrow(\mathrm{r} \wedge \mathrm{s}) \\
& \equiv \sim(\mathrm{p} \wedge \mathrm{q}) \rightarrow(\mathrm{r} \wedge \mathrm{s})
\end{aligned}
\)
\(
\begin{aligned}
& (\sim \mathrm{p} \vee \sim \mathrm{q}) \rightarrow(\mathrm{r} \wedge \mathrm{s}) \\
& \equiv \sim(\mathrm{p} \wedge \mathrm{q}) \rightarrow(\mathrm{r} \wedge \mathrm{s})
\end{aligned}
\)
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