Discrete Mathematics

--------------------------SYMBOLIC

LOGIC

49

This is actually

at

the heart

of

logic. (Some) English arguments

can

be

translated into Boolean expres-

sions, and then

we

can apply rules

of

logic to determine whether the arguments make sense, atleast, based

on

their form.

We

know that Boolean variables are the building blocks

of

Boolean expressions. Boolean variables

like

p generally stand for either English

or

mathematical propositions.

Definition A proposition is something that is either true

or

false

but

not both.

Not all English sentences are propositions.

For

example, the sentence "Run away" cannot really be

said

to

be true

nor

false. Not