Section 1.3

Materials

• Handout
• Lecture Slides

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