E.Math - 1001
Mathematical Logic
Statements and Logical Operators
Presented
By
Daw Nanda Su Hlaing
Assistance Lecturer
Yangon University of Economic
Statement :
A statement or propositions is any declarative sentence
which is either true (T) or false(F). We refer to T or F as
the truth value of the statement. Statements are denoted
by p ,q , r….
Statement
1. Sun rises in East
2. 2+2= 5
Not Statement
1. The number is 5.
2. Solve the following
equation for x.
Compound Statement and Truth Table
• Compound statements
If a statement is the combination of two or more simple
statements, then it is called a compound statement.
Truth table for Negation
P
T
F
F
T
Truth table for Conjunction
p
T
T
F
F
q
T
F
T
F
T
F
F
F
• Truth table for disjunction
p
T
T
F
F
q
T
F
T
F
T
T
T
F
Truth table for conditional
p
T
T
F
F
q
T
F
T
F
T
F
T
T
Truth table for biconditional
p
T
T
F
F
q
T
F
T
F
T
F
F
T
Logical Equivalence
•
Quick Example
same
p
T
F
F
T
T
F
Important Logical Equivalences
•
Tautologies, Contradictions, and
Arguments
Tautologies and Contradictions
A compound statement is a tautology if its truth value is
always T, regardless of the truth values of its variables. It is a
contradiction if its truth value is always F, regardless of the
truth values of its variables.
Quick Example
•
p
T
F
F
T
T
T
all T’s
•
p
T
F
F
T
F
F
Argument
•
q
p
q
T
T
T
T
T
T
F
F
T
F
T
F
F
T
T
F
F
T
F
T
all T’s
p
q
T
T
T
T
T
T
F
F
T
F
T
F
T
T
F
F
F
T
F
T
REFERENCE