When does it not lie? (Boolean Algebra)

Algebra Level 1

When is the Boolean expression $(\neg p) \wedge (\neg q)$ true?

When

p

is false and

q

is true When

p

and

q

are both true When

p

and

q

are both false When

p

is true and

q

is false

1 solution

Ashish Menon
Apr 22, 2016

When p and q are false, their negations would be true and the ^ operator gives a valid expression only when all parts of the sentence are true. So, the final answer is that both p and q are false.

Alternatively, we can use de morgan's laws .

$(\neg p) \wedge (\neg q)$ is identical to $\neg (p \vee q)$ .

$\neg (p \vee q)$ is true when $(p \vee q)$ is false, which happens if and only if both $p$ and $q$ are false.

Pranshu Gaba - 5 years, 1 month ago

Yes, :+1: :)

Ashish Menon - 5 years, 1 month ago

When does it not lie? (Boolean Algebra)

1 solution

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