Algebra of Relations

IMPORTANT

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

EASY
IMPORTANT

Let * be a binary operation on N given by   a*b=HCF(a,b),bN.

The value of   22*4 would be:

EASY
IMPORTANT

Consider the binary operation   *:R×RR and   o:R×RR defined as   a*b=| ab | and   aob=a for all   a,bR.

What does it show:

EASY
IMPORTANT

The binary operation *R×RR, is defined as  a*b=2a+b. From the given options choose the value of  2*3*4 is equal to

MEDIUM
IMPORTANT

Among the two statements

S1:pqp~q is a contradiction and S2:pq~pqp~q~p~q is a tautology

EASY
IMPORTANT

Let A=2,3,4 and B=8,9,12. Then the number of elements in the relation  R=a1,b1,a2,b2A×B,A×B:a1 divides b2 and a2 divides b1 is

EASY
IMPORTANT

Let A=0,3,4,6,7,8,9,10 and R be the relation defined on A such that Rx,yA×A:x-y is odd positive integer or x-y=2. The minimum number of elements that must be added to the relation R, so that it is a symmetric relation, is equal to _________

EASY
IMPORTANT

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

MEDIUM
IMPORTANT

Let A and B be two smallest sets such that A1=1,2,3,4 and B5=4,5,6,7,8. If P=A-B and Q=B-A, then the number of relations from P to Q is

EASY
IMPORTANT

let * be a binary operation on Rdefined by a*b=a4+b7,a,bR.Show that * is not commutative and associative.

EASY
IMPORTANT

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

EASY
IMPORTANT

Show that subtraction and division are not binary operations on N.

EASY
IMPORTANT

A=3,9B=9,6 and C=3,6. Verify associative property of Cartesian product of sets.

EASY
IMPORTANT

A=1,4B=4,5 and C=1,5. Verify associative property of Cartesian product of sets.

EASY
IMPORTANT

A=1,2B=2,3 and C=1,3. Verify associative property of Cartesian product of sets.

EASY
IMPORTANT

If A=5,9B=6,8 and C=9,7, then prove that, A×(BC)=(A×B)(A×C).

EASY
IMPORTANT

If A=b,aB=c,e and C=a,d, then prove that, A×(BC)=(A×B)(A×C).

EASY
IMPORTANT

If A=0,1B=2,4 and C=1,3, then prove that, A×(BC)=(A×B)(A×C).

EASY
IMPORTANT

Suppose * be the multiplication operation and # be the addition operation defined on Z. Let a=10,b=11 and c=12, then find a*(b#c).

EASY
IMPORTANT

Suppose * be the multiplication operation and # be the addition operation defined on Z. Let a=5,b=6 and c=8, then find a*(b#c).

EASY
IMPORTANT

Suppose * be the multiplication operation and # be the addition operation defined on Z. Let a=3,b=4 and c=7, then find a*(b#c).