KCET · Maths · Mathematical Reasoning
The converse of the contrapositive of the conditional \(\mathrm{p} \rightarrow \sim \mathrm{q}\) is
- A \(\mathrm{p} \rightarrow \mathrm{q}\)
- B \(\sim \mathrm{p} \rightarrow \sim \mathrm{q}\)
- C \(\sim \mathrm{q} \rightarrow \mathrm{p}\)
- D \(\sim \mathrm{p} \rightarrow \mathrm{q}\)
Answer & Solution
Correct Answer
(D) \(\sim \mathrm{p} \rightarrow \mathrm{q}\)
Step-by-step Solution
Detailed explanation
The contrapositive of \(\mathrm{p} \rightarrow \sim \mathrm{q}\) is
\[
\sim(\sim \mathrm{q}) \rightarrow \sim \mathrm{p} \text { or } \mathrm{q} \rightarrow \sim \mathrm{p}
\]
Also, converse of \(\mathrm{q} \rightarrow \sim \mathrm{p}\) is \(\sim \mathrm{p} \rightarrow \mathrm{q}\)
\[
\sim(\sim \mathrm{q}) \rightarrow \sim \mathrm{p} \text { or } \mathrm{q} \rightarrow \sim \mathrm{p}
\]
Also, converse of \(\mathrm{q} \rightarrow \sim \mathrm{p}\) is \(\sim \mathrm{p} \rightarrow \mathrm{q}\)
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