ITPEC FE Morning October 2020 Question 2
Source exam: ITPEC FE Morning October 2020Topic: Basic Theory & Math
ITPEC FE Morning October 2020 — Question 2 of 80
Boolean Contradiction — find the expression that is always FALSE.
Simplify (a) (p · (p̄ + q)) · q̄:
- •Distribute:
(p·p̄ + p·q) · q̄ - •
p·p̄ = 0, so:(0 + p·q) · q̄ = p·q·q̄ - •
q·q̄ = 0, so the entire expression = 0
Why not others:
- (b) (p · q̄) · (p̄ + q̄) = p · q̄ when p=1, q=0 → equals 1
- (c) p + (p · q) = p by absorption → TRUE when p=1
- (d) p̄ + (p · q̄) + q → TRUE when p=0
Key rule: Look for x · x̄ = 0 patterns — if the whole expression reduces to a product containing such a pair, it is a contradiction.
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