Discrete Mathematics

72 DISCRETE

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

1.20

APPLICATIONS OF BOOLEAN EXPRESSIONS

One reason

we

study logic is to use it as a tool for reasoning. Propositional calculus (calculating with propo-

sitions, i.e., Boolean expressions) gives us a way, to deduce new

"facts", given that certain facts are already

true.

An

example

of

a rule

of

deduction is modus ponens. Modus ponens says that

if

p and (p

~

q) are both

true, then it follows that

q is true. Logic provides the rules which tell us which conclusions are reasonable to

make, given that certain facts are already true.

It is easy to believe that studying logic is just like studying ...