RELATION FUNCTIONS

1. Submitted to:- Submitted by:-
Dr. Madan Mohan Sati Garishma Bhatia
B.Tech – III sem
Seminal Presentation
Topic:- Relations

2.  Relations are useful when studying properties of
things.There are plenty of areas in theoretical
computer science that require the use of
relations.
 In fact, a graph can be looked as a way of
interpreting relations.This is so because the edge
set is a subset ofV×V.
 Relations are also useful in topics like game
theory and logic.

3.  Let A & B be sets.
 A binary relation from A to B is a
subset of A x B.
 Let R be a relation. If ( a, b )  R, we
write a R b.

4.  A relation on a set A is a relation fromA to A.
 Examples of relations on R:
 R1 = { (a, b) | a  b }.
 R2 = { (a, b) | b = +sqrt( a ) }.
 Are R1 & R2 functions?

5. A relation R onA is:
 Reflexive: a ( aRa ).
Are either R1 or R2 reflexive?
 Symmetric: a b ( aRb  bRa ).
 Let S be a set of people.
 Let R &T be relations on S,
R = { (a, b) | a is a sibling of b }.
T = { (a, b) | a is a brother of b }.
Is R symmetric?
IsT symmetric?

6.  Antisymmetric:
1. a b ( ( aRb  bRa )  ( a = b ) ).
2. a b ( ( a  b )  ( ( a, b )  R  ( b, a )  R ) ).
Example: L = { ( a, b ) | a  b }.
Can a relation be symmetric & antisymmetric?
 Transitive:
a b c ( ( aRb  bRc )  aRc ).
Are any of the previous examples transitive?

7.  It is useful studying properties of thing.
 There are plenty of areas in theoritical computer science
that require the use of relations.
 In fact, a graph can be looked as away of interpreting
relations.This is so because the edge set is a subset of
V×V.
 Relations are also useful in topics like game theory and
logic.

8. THANK
YOU