Discrete Mathematical Structures by Pearson

Mathematical Logic and Methods of Proofs 4-13

The last column in Table 4.18 shows that ( p ∨ q) ↔ (q ∨ p) is a tautology as it is true for all

values of propositional variables. Further, the columns for ( p ∨ q) and (q ∨ p) are identical and

hence ( p ∨ q) =

(q ∨ p), that is, ∨ is commutative.

Example 4 Prove that the conditional statement p → q is equivalent to ∼p ∨ q.

Table 4.19 Truth table for p → q and ∼p ∨ q

Column 1 2 3 4 5

p q

p → q

∼p ∼p ∨ q

T T T F T

T F F F F

F T T T T

F F T T T

In Table 4.19, the columns (3) and (5) are identical and hence the result.

4.5.1 Contingency

A statement that can be true or false depending upon the truth values of its ...