CK-12-Pre-Calculus Concepts

http://www.ck12.org Chapter 16. Logic and Set Theory

To negate complex statements that involve logical connectives like or, and, or if-then, you should start by constructing
a truth table and noting that negation completely switches the truth value.
The negation of a conditional statement is only true when the original if-then statement is false.

TABLE16.7:

P Q P→Q ∼(P→Q)

T T T F

T F F T

F T T F

F F T F

The negation of a conjunction is only false when the original two statements are both true.

TABLE16.8:

P Q P∧Q ∼(P∧Q)

T T T F

T F F T

F T F T

F F F T

The negation of a disjunction is only true when both of the original statements are false.

TABLE16.9:

P Q P∨Q ∼(P∨Q)

T T T F

T F T F

F T T F

F F F T

As mathematical sentences become more complex with additional connectives, truth tables and set theory circles are
good ways to interpret when the statements are true and when the statements are false.