Section 1.3
Materials
Vocabulary
 conditional operation (⇒or →)
 conditional proposition
 conditional statement
 hypothesis (antecedent)
 conclusion (consequent)
 converse
 contrapositive
 inverse
 biconditional operation (⇔ or ↔)
Key Ideas
 The conditional operation is like the "if then" in programming. It indicates that when a certain condition is met (called the hypothesis or antecedent) then a certain result must occur (called the conclusion or consequent).
 It's truth table looks like:

p 
q 
p → q 
T 
T 
T 
T 
F 
F 
F 
T 
T 
F 
F 
T 
 The biggest mistake students make with the conditional operator is marking it false when the condition is false. This is incorrect.
 The other way to think about the conditional operator is to remember that p ⇒ q ≡p q
 The other common mistake(s) people make are starting with a conditional statement and assuming its converse or inverse.
 An original conditional statement is only equivalent to it's contrapositive.
 The converse and inverse are equivalent TO EACH OTHER but are not the same as the original conditional or it's contrapositive.
 The biconditional operation is like a conditional statement that is true in both directions.
 That is, if p ⇒ q and q ⇒p then we say that p ⇔ q