Algebra of Relations
Algebra of Relations: Overview
This topic covers concepts, such as, Algebraic Properties of Cartesian Product of Sets, Non-commutative Property of Cartesian Product of Sets, Composition of Relations & Inverse of a Relation etc.
Important Questions on Algebra of Relations
Let be a binary operation on N given by
The value of would be:

Consider the binary operation and defined as and for all
What does it show:

The binary operation is defined as From the given options choose the value of is equal to

Among the two statements
is a contradiction and is a tautology

Let and . Then the number of elements in the relation is

Let and be the relation defined on such that . The minimum number of elements that must be added to the relation so that it is a symmetric relation, is equal to

If is a relation on finite set having elements, then the number of relations on is

Let and be two smallest sets such that and If and , then the number of relations from to is

let be a binary operation on defined by ,.Show that is not commutative and associative.

Show that division is not a binary operation on real numbers. Give one example.

Show that subtraction and division are not binary operations on .

, and . Verify associative property of Cartesian product of sets.

, and . Verify associative property of Cartesian product of sets.

, and . Verify associative property of Cartesian product of sets.

If , and , then prove that, .

If , and , then prove that, .

If , and , then prove that, .

Suppose be the multiplication operation and be the addition operation defined on . Let , then find .

Suppose be the multiplication operation and be the addition operation defined on . Let , then find .

Suppose be the multiplication operation and be the addition operation defined on . Let , then find .
