MTH 714 Lecture Notes - Lecture 1: Logical Consequence, Berliner Verkehrsbetriebe, Formula Atlantic

• School: Ryerson University
• Department: Mathematics
• Course: MTH 714
• Professor: Dejan Delic

Document Summary

Mth 714: construct a formation tree and the truth table for. T q p (q p) ( p (q p)) a. Solution: (a) if such an assignment v exists, we must have v((p (q r)) ( q p)) = t, v( p) = f. This implies that v(p) = t and (t v(q r)) (v( q) f ) = t. T v(q r) = v(q r), and v( q) f ) = (v( q)) which yields. If v(q) = t , v(q r) (v( q)) = t. (v( q)) = t and the equality holds, regardless of the value of v(r). If, on the other hand, v(q) = f , we have v(q r) = f and the implication will be true again, regardless of v(r). If a disjunction is false, both terms bust be false; therefore: v( p q) = f, v(p q) = f.