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[" Show that the relation "R" in the set defined by "N times N" defined by "],[(a,b)R(c,d)" iff "a^(2)+d^(2)=b^(2)+c^(2),AA a,b,c,d in N," is an equivalence relation."]

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Show that the relation R on the set N xx N defined by (a, b)R(c, d) iff a d(b+c)=b c(a+d) is an equivalence relation.

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.

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.

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.

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.

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.

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 union of two equivalence relations is an equivalence relation.

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)].

If R is the relation in N xx N defined by (a, b) R (c,d) if and only if (a + d) =(b + c), show that R is an equivalence relation.

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