Conditional statements
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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 statements1
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
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 a conditional statement

Variations of :

  • Contrapositive:

  • Converse:

  • Inverse:

  • is logically equivalent to its contrapositive

  • Converse is logically equivalent to inverse


Examples of variations
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
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”,