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# Conditional Statements - PowerPoint PPT Presentation

Conditional Statements. 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. Truth table for .

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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.

• 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 :

• Contrapositive:

• Converse:

• Inverse:

• is logically equivalent to its contrapositive

• Converse is logically equivalent to inverse

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.

• “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”,