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## PowerPoint Slideshow about 'Conditional Statements' - noam

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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.

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”

Variations of a conditional statement

Variations of :

- Contrapositive:
- Converse:
- Inverse:
- is logically equivalent to its contrapositive
- Converse is logically equivalent to inverse

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.

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”,

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