Question

If R is a relation on NxN = {(a,b)/a, beN such that if (ab Radia+d=b-
show that R is an equivalence relation​

Answer 1

Answer:

Step-by-step explanation:

Here, (a,b)R(c,d)⇔a+d=b+c for all (a,b),(c,d)∈N×N. First we will check R for reflexive.

For, (a,b)R(a,b),

⇒a+b=b+a, which is true.

So, R is reflexive.

Now, we will check for symmetric.

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

⇒a+d=b+c

⇒b+c=a+d

⇒c+b=a+d

⇒(c,d)R(a,b) is tur.

So, R is symmetric.

Now, we will check R fo transtivity.

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

⇒a+d=b+candc+f=d+e

⇒a−b=c−dandc−d=e−f

⇒a−b=e−f

⇒a+f=b+e

So, (a,b)R(e,f) is true.

∴R is transitive.

As R is reflexive, symmetric and transitive, R is an equivalence relation.