KCET · Maths · Mathematical Reasoning
The inverse of the proposition \((p \wedge \sim q) \rightarrow r\), is
- A \((\sim r) \rightarrow(\sim p) \vee q\)
- B \((\sim p) \vee q \rightarrow(\sim r)\)
- C \(r \rightarrow p \wedge(\sim q)\)
- D \((\sim p) \vee(\sim q) \rightarrow r\)
Answer & Solution
Correct Answer
(B) \((\sim p) \vee q \rightarrow(\sim r)\)
Step-by-step Solution
Detailed explanation
Given proposition is
\((p \wedge \sim q) \rightarrow r...(i)\)
Inverse of Eq. (i) is
\(\begin{aligned}
&\sim(p \wedge \sim q) \rightarrow \sim r \\
&\equiv \sim p \vee q \rightarrow \sim r \\
&\equiv(\sim p) \vee q \rightarrow(\sim r)
\end{aligned}\)
\((p \wedge \sim q) \rightarrow r...(i)\)
Inverse of Eq. (i) is
\(\begin{aligned}
&\sim(p \wedge \sim q) \rightarrow \sim r \\
&\equiv \sim p \vee q \rightarrow \sim r \\
&\equiv(\sim p) \vee q \rightarrow(\sim r)
\end{aligned}\)
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