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Prove that the relation R on the set Nxx...

Prove that the relation `R` on the set `NxxN` defined by `(a ,\ b)R\ (c ,\ d) 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)].

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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)].

Let N be the set of all natural numbers and let R be a relation on N xx N, defined by (a,b)R(c,d)ad=bc for all (a,b),(c,d)in N xx N. Show that R is an equivalence relation on N xx N. Also,find the equivalence class [(2,6)].

Knowledge Check

  • 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.

    A
    Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for statement-1.
    B
    Statement-1 is True, Statement-2 is true, Statement-2 is not a correct explanation for Statement-1.
    C
    Statement-1 is True, Statement-2 is False
    D
    Statement-1 is False, Statement-2 is True.

  • 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.

    A
    Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for statement-1.
    B
    Statement-1 is True, Statement-2 is true, Statement-2 is not a correct explanation for Statement-1.
    C
    Statement-1 is True, Statement-2 is False
    D
    Statement-1 is False, Statement-2 is True.

  • Let R be a relation over the set NxxN and it is defined by (a,b)R(c,d)impliesa+d=b+c . Then R is

    A
    Symmetric only
    B
    Transitive only
    C
    Reflexive only
    D
    Equivalence only

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