Discrete Mathematics

70 DISCRETE

MATHEMATIC..._---------------------------

essentially, the conclusion is already true (anytime the antecedent, i.e., the Boolean expression to the left

of

the arrow is false, the entire implication is true).

We

could use an example in English.

We

could let p be

"I

tell you", q can

be

"You tell Amy" and r

be

"If

you tell Amy, then Bonnie will know", so the conclusion will be

"If

I tell you, Bonnie will know". The

argument is valid,

if

the premise is true.

1.16.6

Dilemma:

Proof

by

Division

into

Cases

(pvq)

(p

~

r)

(q

~

r)

r

This is an interesting argument.

The

first line says that p or q is true.

We

do not know which one, but at