# Propositional Function - Discrete Mathematics - Lecture Slides, Slides for Discrete Mathematics. Islamic University of Science & Technology

## Discrete Mathematics

Description: During the study of discrete mathematics, I found this course very informative and applicable.The main points in these lecture slides are:Propositional Function, Nested Quantifiers, Rules of Inference, Universe of Discourse, Quantified Predicates, Quantified Variables, Existential Quantifier, Universal Quantifier, Predicate Logic and Propositions
Showing pages  1  -  4  of  27
Discrete Mathematics
CS 2610
August 21, 2008
Docsity.com
2
Agenda
Nested quantifiers
Rules of inference
Proofs
Docsity.com
3
Review
A predicate
P
, or propositional function, is a
function that maps objects in the universe of
discourse to propositions
Predicates can be quantified using the universal
quantifier (“for all”) or the existential quantifier
(“there exists”)
Quantified predicates can be negated as follows
¬∀x P(x) x ¬P(x)
¬∃x P(x) x ¬P(x)
Quantified variables are called “bound
Variables that are not quantified are called “free”
Docsity.com
4
Predicate Logic and Propositions
An expression with zero free variables is an
actual proposition
Ex. Q(x) : x > 0, R(y): y < 10
x Q(x) y R(y)
Docsity.com