Home
Class 11
MATHS
Statement-1: The relation R on the set N...

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.

Text Solution

Verified by Experts

The correct Answer is:
No. Inclusion is not symmetric
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise Exercise 2(c )|23 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise Exercise 2 (d)|3 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise Exercise-2(a)|25 Videos

  • PROBABILITY

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos

Similar Questions

Explore conceptually related problems

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.

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)].

The union of two equivalence relations on a set is not necessarily an equivalence relation on the set.

The union of two equivalence relations on a set is not necessarily an equivalence relation on the set.

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

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

If R and S are two equivalence relations on a set A then R nn S is also an equivalence relation on R.

Statement-1: On the set Z of all odd integers relation R defined by (a, b) in R iff a-b is even for all a, b in Z is an equivalence relation. Statement-2: If a relation R on a set A is symmetric and transitive, then it is reflexive and hence an equivalence relation, because (a, b) in Rimplies(b, a)in R" [By symmetry]" (a, b)in R and (b, a) in Rimplies (a,a)in R " [By transitivity]"

Let A={1,2,3,......, 12} and R be a relation in A xx A defined by (a, b) R (c,d) if ad=bc AA(a,b),(c,d) in A xx A . Prove that R is an equivalence relation. Also obtain the equivalence class [(3,4)] .

Let A={1,2,3,......,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 AxA. Prove that R is an equivalence relation.Also obtain the equivalence class [(2,5)].