Lecture Notes
Math 118: Finite Math
Section 1.1: Logic, Propositions, and Truth Tables
“Statements made must be made in a way that is not open to interpretation”
Definition:Logic is analysis, without regard to meaning or context, of the patterns of re asoning
by which conclusions are validly derived from a set of premises.
Declarative Statements are statements known to be either true or false.
Ex: It is Monday.
It is raining outside.
Politicians are evil.
Statements are assigned letters from p onward using the alphabet:
(p, q, r, s, t,…..)
Negation is the opposite of a declarative statements truth value.
Ex:
A) p: Today is Monday. ~p: Today is not Monday.
B) q: The moon is made of cheese. ~q: The moon is not made of cheese.
C) r: 2+3=/= 6; ~r: 2+3 = 6.
D) s: I have at least $10 in my wallet. ~s: I have less than $10 in my wallet.
E) t: All students do their homework.
~t: At least one student does not do homework.
Truth Tables
Truth tables are used to determine or validate the truth of a statement or compound statement.
Definition:Compound statements are joined by connectors and, or, if…then, and if and only if.
When two or more statements are joined by and, we say the statement is a conjunction.
(Symbol for and = ^)
Ex: Today is Monday and it is raining.
The sky is blue and the grass is purple.
When two or more statements are joined by or, we say the statement is disjunction.
(Symbol for or = v)
Ex: Today is Monday or it is raining.
The sky is blue or the grass is purple.
When it comes to assigning truth values to these compound statements, it is important to
understand that there is a big difference between the words and and or:
