Logical Expressions


















What are the Logical Connectives?

	Negation	not ! ~
	Conjunction	and * ^
	Disjunction	or + v
	Implication	->	(conditional)
	Equivalence	<->	(biconditional)

What's a Truth Table?

	P Q  ~P  P^Q  PvQ  P->Q  P<->Q
	T T   F	  T    T    T	   T
	T F   F	  F    T    F	   F
	F T   T	  F    T    T	   F
	F F   T	  F    F    T	   T


















The Conditional (P -> Q)

P is called the hypothesis or antecedent.

Q is called the conclusion or consequent.


Why is the conditional true when the hypothesis is false?

	If you win, I'll give you a cookie.

Why is the contrapositive equivalent to the original statement?

	If I won't give you a cookie, you didn't win.


Why is the inverse not equivalent to the original statement?

	If you don't win, I won't give you a cookie.

Why is the converse not equivalent to the original statement?

	If I'll give you a cookie, you won.


How are these two statements different?

	I'll give you a cookie if you win.
	I'll give you a cookie only if you win.


What other English statements say the same thing as if P then Q?

	P implies Q
	P only if Q
	P is sufficient for Q

	Q if P
	Q is necessary for P

	Your winning implies I'll give you a cookie.
	You won only if I'll give you a cookie.
	Your winning is sufficient for me to give you a cookie.

	I'll give you a cookie if you win.
	Giving you a cookie is necessary for your winning.


















The Biconditional (P <-> Q)

Why is Equivalence also called the Biconditional?

	(P <-> Q) is the same as (P->Q) and (Q->P)

How do you pronounce <-> or iff?

	if and only if

















Translate the sentence into a logical expression. (use R,H,G)


	If berries are ripe along the trail, hiking is safe if and
	only if grizzly bears have not been seen in the area.


















Classwork
You may work with a partner.

Translate the sentence into a logical expression. (use H,G,R)


	Hiking is not safe on the trail whenever grizzly bears have
	been seen in the area and berries are ripe along the trail.