Truth Table

Negation:

The negation or denial of a false statement is a true statement. If you see a "tilde" (~) it means NOT p ~p T F F T

Bi-conditionals (Material Equivalence):

A biconditional is true and only true if and only if its components have the same truth value; otherwise it's false. If you see a "tribar" (≡) it means IF AND ONLY IF p q p≡q T T T T F F F T F F F T

Conjunction

A conjunction of two statements is true if and only if both statements are true. If you see a "dot" (•) it means AND p q p•q T T T T F F F T F F F F

Disjunction

A disjunction is true except when both of its component statements are false. If you see a "wedge" (V) it means EITHER/ OR p q p V q T T T T F T F T T F F F

Material implication (Material Conditional)

A statement of the form "If p, then q." A statement of material implication is true except when its antecedent (if-part) is true and its consequent (then-part) is false. The first part (p) is called the antecedent; the second part (q) is called the consequent. If you see a "horseshoe" (⊃) it means IF, THEN p q p⊃q T T T T F F F T T F F T