Question
Download Solution PDFNegation of the Boolean expression p ⇔ (q ⇒ p) is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation
\(\sim (p \leftrightarrow (q \rightarrow p))\)
⇒ \(\sim (p \leftrightarrow q) = (p \land \sim q) \lor (q \land \sim p)\)
⇒ \(\sim (p \leftrightarrow (q \rightarrow p)) = (p \land \sim (q \rightarrow p)) \lor ((q \rightarrow p) \land \sim p)\)
⇒ \((p \land \sim (q \rightarrow p)) = p \land (q \land \sim p) = (p \land \sim p) \land q = c\)
⇒ \((q \rightarrow p) \land \sim p = (\sim q \lor p) \land \sim p = \sim q \land \sim p = \sim p \land \sim q\)
\(= (\sim p \land \sim q) \lor (\sim p \land p) = \sim p \land \sim q\)
⇒ \(\sim (p \leftrightarrow (q \rightarrow p)) = c \lor (\sim p \land \sim q) = \sim p \land \sim q\)
Hence option 4 is correct
Last updated on Jul 3, 2025
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