Download Biconditional Statements

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.