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.
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
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
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