Logic and Proofs

Walkthrough

Construct a truth table for p ∧ (q ∨ ¬p).

1. 1.A truth table evaluates a logical expression for all possible truth values of its variables. With two variables p and q, there are 4 rows.
2. 2.List all combinations: (T,T), (T,F), (F,T), (F,F).
3. 3.Compute ¬p for each row: F, F, T, T.
4. 4.Compute q ∨ ¬p: (T∨F)=T, (F∨F)=F, (T∨T)=T, (F∨T)=T.
5. 5.Compute p ∧ (q ∨ ¬p): (T∧T)=T, (T∧F)=F, (F∧T)=F, (F∧T)=F. So the column is T, F, F, F.