This document provides an overview of quantifiers in discrete mathematics. It defines a quantifier as an operator used to create a proposition from a propositional function. The universal quantifier indicates that a propositional function is true for all values in the universe of discourse, while the existential quantifier indicates there exists at least one value for which the propositional function is true. The document provides examples of universal and existential quantification using the propositional function P(x) = "x^2 < 10" over the universe of positive integers not exceeding 4.

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