Question

Q)37. Show that the relation R is defined by (a,b) R (c,d) <=> a + d = b + c on the set N X N is an equivalence relation​

Answer 1

Step-by-step explanation:

ad=bc in an equivalence relation.

Symmetric:

if (a,b)R(c,d)∈N×N

⇒ad=bc

⇒bc=ad

⇒(c,d)R(a,b)

R is symmetric

Reflexive:

If (a,b)∈N×N

⇒ab=ab

(a,b)∈(a,b) . So R is reflexive.

Transitive:

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

⇒ad=bc and cf=de

⇒

b

a

=

d

c

and

d

c

=

f

e

⇒

b

a

=

f

e

af=eb

(a,b)R(e,f)∈N×N

So R is transitive

Therefore R is in equivalence relation.

Answer 2

hope you understand the answer