COT 3100 Sec. #7094X
Brief Review of Lecture #2

In lecture 2 we continued learning about propositional logic. We introduced the following new logical operators, and learned how propositions involving these operators can be equivalently expressed in a variety of different ways.

Name: Symbol: Usage: Meaning of example: Some equivalences:
Exclusive ORp q"Either p or q, but not both, is true." (p \/ q) /\ ¬(p /\ q)
Implies p q "If p is true, then q is also true." ¬p \/ q
¬(p /\ ¬q)
¬q ¬p
Biconditional p q "p is true if and only if q is true." (p q) /\ (q p)
¬(p q)

The truth tables for these operators are as follows:

Cases  Truth values of...
# p q   p q p q p q
0 F F  F T T
1 F T  T T F
2 T F  T F F
3 T T  F T T