CS381 Notes

Posted in cs381 by bnmng on 2012 08/30

Chapter 1: Foundations of Logic


Mathematical logic includes a formal language, precice notation.

Propositional Logic is the logic of compound statements using boolean connectives.

A proposition is a declarative statement that is either true or false.  Propositional logic includes combining propositions with connectives (also called operators).

Understand the contrapositive.  Reverse each element, then switch them.  The contrapositive has the same truth table as the original.



a) Swimming is not allowed or there are sharks.

b) swimming is allowed only if there are no sharks

( p can-imply q ) and ( not p can imply q )

Swimming is allowed can imply that there are sharks, AND swimming is not allowed can imply that there are sharks

p  q | !p    p->q     !p->q    p->q^!p->q
1 1    0        1              1                    1
1 0    0        0             0                    0
0 1    1         1              1                   1
0 0    1        1              0                   0


If two compound statements have the same truth table, they are equivalent.



Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )


Connecting to %s

%d bloggers like this: