Quantifer Made by saliha shaheen

1. PRESENTATION
DISCREET MATHMATICS
NAME :SALIHASHAHEEN
ROLL NO:19104009-048
SUBMITTED TO:SIR
MUHAMMAD AHSAN
KHAN

2. Quantifiers
• What is Quantifier?
• What is UniversalQuantifier?
•What isExistentialQuantifier?

3. x>3
Ali ki desk py book pari hogi shyd
Proposition:
Can be true or false
EXAMPLE:i
Predicate
Can not be true or false
Until value is not assigned
to variable
EXAMPLE:
w •
I I ki I I I/4 me
NOTE:
Predicate becomes Proposition
If value is assigned to variable
REPRESENTATION:
Propositional function P(x)
P(x) : x>3
If P(x) is x > 3, then what
Is truth value of P(4)=4>3
TRUE

4. QUANTIFIER
A quantifier is an operator used to create a
proposition from a propositional function, An
other
way, if we do not assign values to p(x)
UNIVERSAL QUANTIFIER
P(x) is true For all values of x in
P(x)=X<5
Values not exceeding 4
Universe of discourse
(1. e range)' r
The universe of discourse
representation
EXISTENTIAL Quantification
There exists a value of x in the
universe of discourse such that f-( x)
is true
REPRESENTATION
∃xp(x)
∀x P(x

5. EXAM PLE:
What is the truth value of ∀x P(x), where P(x) is the statement
"x^2<10
"
and the universe of discourse consists of positive integers not
exceeding 4?
ANSWER
0^2<10 1^2<10 2^2<10 3^2<10 4^2<10
0<10 1<10 4<10 9<10 16<10

6. e
What is the truth value of ∀x P(x, where P(x) is the statement "x^2<10 '
and the universe of discourse consists of positive integers not
exceeding 4?
FLASE
0^2<10 1^2<10 2^2<10 3^2<10 4^2<10
0<10 1<10 4<10 9<10 16<10
What is the truth value of ∃xp(x, where P(x) is the statement x^2 <1 0"
and the universe of discourse consists of positive integers not
exceeding 4?
True 0^2 < 10
0<10