Q. 114.7( 3 Votes )

# Let A = {1, 2, 3,

Answer :

Given that, A = {1, 2, 3, ... 9} and R be the relation in A ×A defined by (a, b) R (c, d) if a + d = b + c for (a, b), (c, d) in A ×A.

Reflexivity:

Let (a,b) R (a,b)

a+b = b+a

which is true since addition is commutative on N.

R is reflexive.

Symmetricity:

Let (a,b) R (c,d)

a+d = b+c

b+c = a+d

[since addition is commutative on N]

c+b = d+a

(c,d) R (a,b)

R is symmetric.

Transitivity:

Let (a,b) R (c,d) and (c,d) R (e,f)

a+d = b+c and c+f = d+e

(a+d) – (d+e) = (b+c ) – (c+f)

a-e= b-f

a+f = b+e

(a,b) R (e,f)

R is transitive.

Hence, R is an equivalence relation.

Equivalence class [(2,5)]

Let (a,b) R (2,5)

a+5 = b+2

a-b = 2-5

= -3

Hence,

The equivalence class [(2,5)] = {(1,4),(2,5),(3,6),(4,7),(5,8),(6,9)}

In general,

{(a,a+3)|a A}

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

Fill in theMathematics - Exemplar

State True Mathematics - Exemplar

State True Mathematics - Exemplar

State True Mathematics - Exemplar

Let A = {1, 2, 3}Mathematics - Exemplar

Show that the relMathematics - Board Papers

Let N denote the Mathematics - Board Papers