Types of Argument (Logical operators)

By:Mujtaba Khan

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.

Types of logical Operators

• Negation• Conjunctions• Disjunctions• Conditional• Bi-conditional

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

Truth Table for Negation

PTF

~PFT

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.

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

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.

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

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.

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

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

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

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