This document defines and explains different types of logical operators: negation, conjunctions, disjunctions, conditionals, and bi-conditionals. It provides examples of each operator and includes their truth tables showing how the operators evaluate statements as true or false based on the truth values of the individual statements.

1. Types of Argument
(Logical operators)
By:Mujtaba Khan

2. Logical Operators
• In logic, a logical operators (also called
a logical connectives) is
a symbol or word used to connect two or
more sentences in a grammatically valid way.

3. Types of logical Operators
• Negation
• Conjunctions
• Disjunctions
• Conditional
• Bi-conditional

4. Negation
• Changing a statement so that it has the opposite meaning and
truth values
• Also known as “Not”
• The symbol for negation is ‘~’
• Example:
P: There is snow on the ground
~P: There is not snow on the ground

5. Truth Table for Negation
P
T
F
~P
F
T

6. Conjunctions
• A proposition that presents two or more alternative
terms, with the assertion that both are true.
• Also known as And.
• symbol that we use is ‘^’ (Looks like an A without the
middle line – ).
• Example:
– P: I found $5
– Q: I crashed my car into a telephone pole
– P^Q: I found $5 AND I crashed my car into a telephone pole.

7. Truth Table for “And”
• A conjunction is only true if all of the
statements in it are true, otherwise it is
false
P Q P^Q
T T T
T F F
F T F
F F F

8. Disjunctions
• A proposition that presents two or more
alternative terms, with the assertion that at
least one is true.
• Also known as “Or”
• symbol that we use is ‘V’
• Example:
– P: The number 3 is odd
– Q: 57 is a prime number
– PVQ: The number 3 is odd OR 57 is a prime number.

9. Truth Table for “Or”
• A disjunction is true if at least one of
the statements in it are true, otherwise
it is false.
P Q PVQ
T T T
T F T
F T T
F F F

10. Conditionals
• An conditional is only false when the first statement
is true and the second one is false, otherwise it is
true.
• Also known as an “If-Then” Statement
• An Conditional for statements P and Q is denoted P=>
Q
• An Conditional is read either “If P, then Q” or “P
implies Q”
• Example: If you brush every day, you probably won’t
get cavities or gum disease.

11. Truth Table for “If-Then”
• An conditional is only false when the
first statement is true and the second
one is false, otherwise it is true.
P Q P=>Q
T T T
T F F
F T T
F F T

12. Bi-conditional
• Bi-conditionals are true when both
statements have the exact same truth
value.
• Also known as “ If and only If ”
• An Biconditional for statement P and Q is
denoted by P<=> Q
• An Bi-conditional is read “P if and only if Q”
• Example: The candidate becomes president
if and only if he wins the election

13. Truth Tables for Biconditional
P Q P<=>Q
T T T
T F F
F T F
F F T
A Bi-conditional is only true when the truth
values of ‘P’ and ‘Q’ are the same

14. THANK YOU