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  • The negation of the Boolean expression <img alt="\mathrm{((\sim q) \wedge p) \Rightarrow((\sim p) \vee q)}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%28%28%5Csim%20q%29%20%5

The negation of the Boolean expression \mathrm{((\sim q) \wedge p) \Rightarrow((\sim p) \vee q)} is logically equivalent to :

Option: 1

\mathrm{p \Rightarrow q} \\


Option: 2

\mathrm{q \Rightarrow p} \\


Option: 3

\mathrm{\sim(p \Rightarrow q)} \\


Option: 4

\mathrm{\sim(q \Rightarrow p)}


Answers (1)

best_answer

To find negation of \mathrm{((\sim q \wedge p) \rightarrow((\sim p) \vee q)}

Let  \mathrm{\sim q \wedge p=A \& \sim p \forall q=B }\\

      \mathrm{\sim(A \rightarrow B)=\sim(\sim A \vee B)=A \wedge \sim B} .

Using abve formulae we get

\mathrm{(\sim q \wedge p) \wedge \sim(\sim p \vee q)=(\sim q \wedge p) \wedge(p \wedge \sim q) }\\

\mathrm{=A \wedge A=A=\sim q \wedge p=p \wedge \sim q \: o r \sim(p \rightarrow q)}

Hence the correct answer is option 3

Posted by

rishi.raj

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