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  • Which of the following is equivalent to the Boolean expression ?  Option: 1 <img alt="\sim \mathrm{p} \rightarrow \sim \mat

Which of the following is equivalent to the Boolean expression p \wedge \sim q ?
 
Option: 1 \sim \mathrm{p} \rightarrow \sim \mathrm{q}
Option: 2 \sim(q \rightarrow p)
Option: 3 \sim(p \rightarrow q)
Option: 4 \sim(p \rightarrow \sim q)

Answers (1)

best_answer

Option 1 . \sim p\rightarrow \sim q
            \equiv \sim \left ( \sim p \right )\vee \sim q
           = p\vee \sim q
Option 2. \sim \left ( q\rightarrow p \right )
            \equiv \sim \left ( \sim q\vee p \right )
            \equiv q\wedge \sim p
Option 3. \sim \left ( p\rightarrow q \right )
             \equiv \sim \left ( \sim p\vee q \right )
             \equiv p\wedge \sim q
so option (3)  

Posted by

Kuldeep Maurya

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