Conditional Statements

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Conditional Statements
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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.

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Truth table for
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Logical equivalences including

• Example of the first equivalence
• Either Jim works hard
• or he gets F
• is equivalent to
• If Jim doesnt work hard
• then he gets F

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Variations of a conditional statement

• Variations of
• Contrapositive
• Converse
• Inverse
• is logically equivalent to its
  contrapositive
• Converse is logically equivalent to inverse

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Examples of variations

• If Bobcats win this game,
• then they will be number one.
• Contrapositive If Bobcats arent 1
• then they didnt win.
• Converse If Bobcats are number one
• then they won the game.
• Inverse If Bobcats dont win this game
• then they will not be 1.

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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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Summary of conditional statements
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Order of operations