Aspire Faculty ID #19224 · Topic: UGC NET Computer Science June 2019 (Paper II) · Just now
UGC NET Computer Science June 2019 (Paper II)

Which of the following is principal conjunctive normal form for $[(p \vee q)\wedge[p \to q]]$?

Solution

Given statement is

$[(p \vee q)\wedge[p \to q]]$

We know that

$p \to q \equiv \neg p \vee q$

So,

$[(p \vee q)\wedge[p \to q]]=(p \vee q)\wedge(\neg p \vee q)$

Now truth table se false cases:

When $p=0,\ q=0$, expression false hoti hai.
Corresponding maxterm is

$p \vee q$

When $p=1,\ q=0$, expression false hoti hai.
Corresponding maxterm is

$\neg p \vee q$

Therefore, PCNF is

$(p \vee q)\wedge(\neg p \vee q)$

Hence, correct PCNF is $(p \vee q)\wedge(\neg p \vee q)$.

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