CONJUNCTION

Definition : A conjunction is a compound statement formed by joining two statements with the connector AND. The conjunction "p and q" is symbolized by p ˄ q. A conjunction is true when both of its combined parts are true; otherwise it is false. With a conjunction, both statements must be true for the conjunction to be true.

Example 1: Statement p represents the sentence, "Ann is on the softball team," and  statement q represents the sentence, "Paul is on the football team." The symbol ˄  is a logical connector which means "and." Therefore, the compound statement  p ˄ q represents     the sentence, "Ann is on the softball team and Paul is on  the footballteam." The statement p ˄ q is a conjunction. p q p ˄ q T T T T F F F T F F F F Example 2: Given: a: A square is a quadrilateral. b: Harrison Ford is an American actor. Problem:  Construct a truth table for the conjunction "a and b." Solution: a b a ˄ b T T T T F F F T F F F F Example 3: Given: r: The number x is odd. s: The number x is prime. Problem: Can we list all truth values for r ˄ s in a truth table?Why or why not? Solution:  If x = 3, then r is true, s is true. The conjunction r ˄ s is true. If x = 9, then r is true, s is false. The conjunction r ˄ s is false. If x = 2, then r is false, s is true. The conjunction r ˄ s is false. If x = 6, then r is false, s is false. The conjunction r ˄ s is false.