ITPEC FE Morning October 2019 Question 1

It reduces to NOT p OR p, which is always 1 — simplify each expression with Boolean algebra; only one collapses to the constant 1.

Here + is OR, · is AND, and a bar is NOT. In option (b), factor p out of the two AND terms that contain it:

(p · q) + (p · q) = p · (q + q) = p · 1 = p

So the whole expression is p + p, which is 1 for every value of p and q: a tautology.

Answer (b)

Why not others:

• •(a) — simplifies to p + q, which is 0 when p = 1 and q = 0
• •(c) — expands to p · q · p + p · q · q; each term ANDs a variable with its own negation, so the expression is always 0, the opposite of what is asked
• •(d) — contains p · q · p, and p · p = 0, so the whole AND chain is always 0

Key rule: An expression is always true when it reduces to x + x; if in doubt, test all 2ⁿ input rows, and a single 0 rules it out.

Basic Theory · AI-written, may contain errors