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If R is a relation on NxxN defined by (a...

If R is a relation on `NxxN` defined by (a,b) R (c,d) iff a+d=b+c, then

A

Symmetric only

B

Transitive only

C

Reflexive only

D

Equivalence only

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The correct Answer is:
D
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Let N be the set of all natural numbers and let R be a relation on N×N , defined by (a , b)R(c , d) iff a d=b c for all (a , b),(c , d) in N × Ndot . Show that R is an equivalence relation on N × N .

Let N be the set of all natural numbers and let R be a relation on NxxN , defined by (a ,\ b)R\ (c ,\ d) a d=b c for all (a ,\ b),\ (c ,\ d) in NxxN . Show that R is an equivalence relation on NxxN

Let N denote the set of all natural numbers and R be the relation on N xx N defined by (a , b)R(c , d) iff a d(b+c)=b c(a+d) . Check whether R is an equivalence relation on N xx N

Let N denote the set of all natural numbers and R be the relation on NxN defined by (a , b)R(c , d) iff a d(b+c)=b c(a+d)dot Check whether R is an equivalence relation on NxNdot

Let R be a relation on NxxN defined by (a , b)\ R(c , d)hArra+d=b+c\ if\ (a , b),(c , d) in NxxN then show that: (i)\ (a , b)R\ (a , b)\ for\ a l l\ (a , b) in NxxN (ii)\ (a , b)R(c , d)=>(c , d)R(a , b)for\ a l l\ (a , b),\ (c , d) in NxxN (iii)\ (a , b)R\ (c , d)a n d\ (c , d)R(e ,f)=>(a , b)R(e ,f)\ for all \ (a , b),\ (c , d),\ (e ,f) in NxxN

Statement-1: The relation R on the set N xx N defined by (a, b) R (c, d) iff a+d = b+c for all a, b, c, d in N is an equivalence relation. Statement-2: The intersection of two equivalence relations on a set A is an equivalence relation.

Let A={1,\ 2,\ 3,\ ,\ 9} and R be the relation on AxxA defined by (a ,\ b)R\ (c ,\ d) if a+d=b+c for all (a ,\ b),\ (c ,\ d) in AxxA . Prove that R is an equivalence relation and also obtain the equivalence class [(2, 5)].

Let A={1,\ 2,\ 3,\ ,\ 9} and R be the relation on AxxA defined by (a ,\ b)R\ (c ,\ d) if a+d=b+c for all (a ,\ b),\ (c ,\ d) in AxxA . Prove that R is an equivalence relation and also obtain the equivalence class [(2, 5)].

Prove that the relation R on the set NxxN defined by (a ,\ b)R\ (c ,\ d) iff a+d=b+c for all (a ,\ b),\ (c ,\ d) in NxxN is an equivalence relation. Also, find the equivalence classes [(2, 3)] and [(1, 3)].

Let A={1,2,3,ddot,9} and R be the relation in AxA defined by (a ,b)R(c ,d) if a+d=b+c for (a ,b),(c , d) in AxAdot Prove that R is an equivalence relation. Also obtain the equivalence class [(2,5)].

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