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3 years ago

Use a truth table to verify the ﬁrst De Morgan law (p ∧ q)’ ≡ p’ ∨ q’.

Mathematics

1 answer:

Nutka1998 [239]3 years ago

6 0

Answer:

(p ∧ q)’ ≡ p’ ∨ q’

Step-by-step explanation:

First, p and q have just four (4) possibilities, p∧q is true (t) when p and q are both t.

p ∧ q

t t t

t f f

f f t

f f f

next step is getting the opposite

(p∧q)'

f

t

Then we get p' V q', V is true (t) when the first or the second is true.

p' V q'

f f f

f t t

t t f

t t t

Let's compare them, ≡ is true if the first is equal to the second one.

(p∧q)' ≡ (p' V q')

f f

t t

Both are true, so

(p ∧ q)’ ≡ p’ ∨ q’

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From the question we are told that

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