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Biconditional Statements Logic Biconditionals • A biconditional is the conjunction of a conditional and its converse. Conditional: (p → q) Converse: (q → p) Biconditional: (p → q) Λ (q → p) In other words: p ↔ q Read: p if and only if q. Biconditionals • p: the sides of a triangle are congruent. q: the angles are congruent. • Conditional: p → q If the sides of a triangle are congruent, then the angles are congruent. • Converse: q → p If the angles are congruent, then the sides of the triangles are congruent. • Biconditional: p ↔ q The sides of a triangle are congruent if and only if the angles are congruent. Example • The statement “I go to basketball practice on Monday and Thursday” is true. • p: Today is Monday • q: I go to basketball practice p q T T T F F T F F p →q q →p (p → q) Λ (q → p) p↔q Example • Determine the truth value of the following biconditional: 3y + 1 = 28 if and only if y = 9 When y = 9, 3y + 1 = 28 is true and y = 9 is true. Therefore, 3y + 1 = 28 if and only if y = 9 is true. When y ≠ 9, 3y + 1 = 28 is false and y = 9 is false. Therefore, 3y + 1 = 28 iff y = 9 is always true.