1. Conditional Statements

2. Conditional statements
Form of conditional statement:
If p then q (p implies q)
Denote by
p is called hypothesis, q is called conclusion
Ex: If Bobcats win this game,
then they will be number one.

3. Truth table for p q T F

4. Logical equivalences including
Example of the first equivalence:
“Either Jim works hard
or he gets F”
is equivalent to
“If Jim doesn’t work hard
then he gets F”

5. Variations of a conditional statement
Contrapositive:
Converse:
Inverse:
is logically equivalent to its contrapositive
Converse is logically equivalent to inverse

6. Examples of variations
If Bobcats win this game,
then they will be number one.
Contrapositive: If Bobcats aren’t #1
then they didn’t win.
Converse: If Bobcats are number one
then they won the game.
Inverse: If Bobcats don’t win this game
then they will not be #1.

7. Other conditional statements
“q only if p” means
“if not p then not q”
or, equivalently, “if q then p”
“q if and only if p” means
Other ways to say or to denote it:
“biconditional of p and q”,
“q iff p”,

8. Summary of conditional statements
original statement
converse statement
biconditional statement
if p then q
q only if p
q if and only if p
p is sufficient condition for q
p is necessary condition for q
p is necessary and sufficient for q

9. Order of operations