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Presented by: Tutorial Services The Math Center Truth Tables Presented by: Tutorial Services The Math Center

Truth Tables ~ ~p “And” p q “Or” A truth table is a device used to determine when a compound statement is true or false. Connectives used in truth tables: Formal Name Symbol Read Symbolic Form Negation ~ “Not” ~p Conjunction “And” p q Disjunction “Or” Conditional “If-then” Bi-conditional “If and only If”

Types of Arguments When finding the truth value of a Conjunction When finding the truth value of a conjunction, all values must be true in order for the entire conjunction to be true. For example, if p and q are true, then (p  q) is true. For example, if p is true and q is false, (p  q) is false. For example, if p and q are false, then (p  q) is false. p q T F

Types of Arguments When finding the truth value of a Disjunction When finding the truth value of a disjunction, only one value needs to be true in order for the entire disjunction to be true. For example, if p is true and q is false, then (p  q) is true. For example, if both p and q are true, For example, if both p and q are false, then (p  q) is false. p q T F

Types of Arguments The truth values of ~p are exactly Negation The truth values of ~p are exactly the opposite truth values of p. For example, true for p would be false for ~p. For example, false for (p  q) would be true for ~(p  q). p ~p T F

Types of Arguments When finding the truth value of a Conditional When finding the truth value of a conditional statement, same values will be true. Otherwise, follow the truth value of the conclusion (which is the second proposition). For example, if p and q are false, then (p  q) is true. For example, if p is true and q is false, then (p  q) is false. For example, if p is false and q is true, then (p  q) is true. p q p q T F

Types of Arguments When finding the truth value of Bi-conditional When finding the truth value of a bi-conditional statement, same values will be true. Otherwise, the truth value will be false. For example, if both p and q are false, then (p  q) is true. For example, if p is true and q is false, then (p  q) is false. For example, if p is false and q is true, then (p  q) is false. p q T F

Examples Example1: p q p  q ~q T F

Examples Example 2: p q r ~r q ~r T F

Examples Example 3: p q r ~r q ~r T F

Truth Tables Links Truth Tables Handout