CHAPTER 1 - LOGIC OF COMPOUND STATEMENTS
1.1 - Logical Form and Logical Equivalence
Definition. A statement or proposition is a sentence that is either true or false, but not both.
ex.
1 + 2 = 3
1 + 4 = 7
x + 4 > 9
X IS a statement
X IS a statement
IS NO

Question 1 (1 point)
Is the following a statement?
What time is it?
Question 1 options:
YES
NO
Save
Question 2 (1 point)
Is the following a statement?
My new dress is red.
Question 2 options:
YES
NO
Save
Question 3 (1 point)
For which integer n is the fol

Math 2120 - Section 1.5 Notes
Tautologies & Contradictions
Tautology
Def 1.59 - Tautology
A compound statement is a tautology if it is true for all possible combinations of truth values
of its component statements.
For Example:
P
T
F
Ex 1.
P
F
T
P ( P)

Math 2120 - Section 1.4 Notes
Biconditionals
If and only if
Def 1.52- Biconditional
For two statements P and Q, the biconditional of P and Q is the conjunction of the implication
P Q and its converse Q P.
The biconditional of P and Q is denoted by P Q. S

Math 2120 - Section 1.3 Notes
Implications
Implication
Def - Implication
For two statements P and Q, the statement If P, then Q ( or P implies Q) is called an
implication of P and Q.
We usually denote this as P Q.
P is the hypothesis, Q is the conclusion

Math 2120 - Section 1.2 Notes
Negation, Conjunction, and Disjunction
The Truth Table
Def - Truth Table
A truth table is a table that gives all possible assignments of truth values for a statement or
statements under consideration.
Statements are usually

Math 2120 - Section 1.1 Notes
Statements
Types of Sentences
Sentences or statements can be divided into four categories:
Declarative sentence - something is being declared or asserted.
For Example: Atlanta is the capital of Georgia.
Interrogative sen

Example:
Use De Morgans laws to find the negation of each of the following statements.
In order to solve, we need to know De Morgans Laws. They are as follows:
~ ( P Q ) ~ P ~ Q
~ ( P Q ) ~ P ~ Q
a). Kwame will take a job in industry or go to graduate sch

3 ,
Discrete Math HW 1 Name: Z - ,
Math 2120 Ch. 1 & 2 . %
Mr. Day Spring, 2016
(25 points) Problem Solving: This assignment is due on review day, February 1st. No late submissions
allowed! Make certain you show your work to receive full credit on each pr