INTRODUCTION TO SENTENTIAL LOGIC
TRUTH FUNCTIONAL SENTENCE CONNECTIVES

Mathematical functions input numbers and output numbers. Anything that gives one certain output for any given input can be called a function.

Sentence connectives are like truth functions because the truth value of a compound sentence (such as A & B) is determined solely by the truth values of its simple claims. That is, if you know whether sentence A and sentence B are true, then you know whether sentence A & B is true.

AND: The truth function for the connective “AND” gives a truth value of true (T) whenever both conjuncts are true and false whenever one of the conjuncts are false (F). For example, if sentence A is true and sentence B is true, then sentence A & B is also true.

OR: The truth function for the connective “OR” gives a truth value of true (T) whenever one of the disjuncts are true and false whenever both disjuncts are false (F). For example, if sentence A is true and sentence B is false, the sentence A V B is true (since only one needs to be true).

IF/THEN: The IF/THEN or IMPLIES connective produces a CONDITIONAL sentence, which connects an antecedent (the condition, after the ‘if’) and a consequent (after the ‘then’) in a particular way. Namely, a conditional sentence asserts that whenever the antecedent is true, so is the consequent. For example, the sentence A  B is true if A is true and B is true. The only way for a