Discrete Mathematics

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SYMBOLIC

LOGIC

69

1.16.2

Disjunctive

Addition

p

(pvq)

All this says is that

if

pis

true, then

we

can always

OR

something

top.

In this case q is

OR'ed

with p to

produce

(p v q). Since

pis

already true (because

we

assumed it to be true since it is part

of

the premise), then

p

OR'ed

with any other variable is also going to be true. (Recall that when we have ($ v 'ljl). either one

of

t1>

or

'ljl can

be

true for the whole expression to be true.)

Note that

we

could have substituted any other variable for p and

q.

For example,

we

could have used

p and r

or

rand

q.

There is no special reason for choosing these two Boolean ...