Discrete Mathematical Structures by Pearson

Mathematical Logic and Methods of Proofs 4-11

XOR Operator: If p and q are two statements, then XOR of p and q denoted by p ⊕ q is a true

statement when either p or q is true but not both and vice versa. The truth values of p ⊕ q are

shown in Table 4.12.

Table 4.12 Truth table for p ⊕ q

p q

p

⊕ q

T T F

T F T

F T T

F F F

4.4.8 Biconditional Statements

If p and q are statements, then the compound statement p if and only if q denoted by p ↔ q

is read as p implies q and is implied by q is called an equivalence or biconditional statement.

The equivalence p ↔ q can also be stated that p is a necessary and sufficient condition for q

(see Table 4.13).

Table ...