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CHAPTER 1 ■ LOGIC: INTRODUCTION 13
Table 1-5. Truth Table for AND (Conjunction)
P Q P ∧ Q
T T T
T F F
F T F
F F F
P ∧ Q is TRUE if and only if both P and Q are TRUE. In all other cases, P ∧ Q is FALSE. In a
conjunction P ∧ Q, P and Q are referred to as the conjuncts.
Table 1-6. Truth Table for OR (Disjunction)
P Q P ∨ Q
T T T
T F T
F T T
F F F
P ∨ Q is FALSE if and only if both P and Q are FALSE. In a disjunction P ∨ Q, P and Q are
referred to as the disjuncts.
■Note The OR operator that is defined here is called the inclusive or. In natural language, we normally refer
to the inclusive or when using the word “or.” However, we sometimes use “or” to denote what is called the
exclusive or (eor for short). Compared to the truth table for the inclusive or (Table 1-6), the truth table for the
exclusive or differs only on the first row; the propositional form P eor Q is FALSE if both P and Q are TRUE.
An example use of the exclusive or is in the statement, “You must clean up your room or you go to bed
early.” Clearly you aren’t required to both clean up your room and go to bed early. In this book we will
always use the inclusive or.
Table 1-7. Truth Table for IF . . . THEN (Implication)
P Q P ⇒ Q
T T T
T F F
F T T
F F T