Home
Class 12
MATHS
Let A={x in Z:0 le x le 12}. Show that R...

Let `A={x in Z:0 le x le 12}`. Show that `R={(a,b):a,b in A,|a-b|is divisible by 4}` is an equivalence relation. Find the set of all elements related to 1. Also write the equivalence class [2]

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise FREQUENTLY ASKED QUESTIONS|15 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise QUESTIONS FROM NCERT EXEMPLAR|5 Videos

  • PROBABILITY

    MODERN PUBLICATION|Exercise MOCK TEST SECTION D|6 Videos

  • THREE DIMENSIONAL GEOMETRY

    MODERN PUBLICATION|Exercise CHAPTER TEST 11|11 Videos

Similar Questions

Explore conceptually related problems

Let A={x in Z:0<=x<=12}. show that R={(a,b):a,b inbar(A),|a-b|is-:isib<=by4} is an equivalence relation.Find the set of all elements related to 1. Also write the equivalence class [2]

Show that the relation R on the set A={x in Z:0<=x<=12}, given by R={(a,b):|a-b| is a multiple of 4} is an equivalence relation.Find the set of all elements related to 1 i.e.equivalence class [1]

Let R={(a,b):a,b in Z and (a-b) is divisible by 5}. Show that R is an equivalence relation on Z.

Show that the relation S in the set A={x in Z:0<=x<=12} given by S={(a,b):a,b epsilon Z,^(-)|a-b| is divisible by 4} is an equivalence relation.Find the set of all elements related to 1.

Show that the relation R on the set A{x in Z;0<=12}, given by R={(a,b):a=b}, is an equivalence relation.Find the set of all elements related to 1.

Show that each of the relation R in the set A={x in Z:0<=x<=12} given by (i) R={(a,b):|a-b| is a multiple of 4} (ii) quad R={(a,b):a=b} is an equivalence relation.Find the set of all elements related to 1 in each case.

Show that the relation R on the set A={x in Z;0<=x<=12}, given by R={(a,b):a=b}, is an equivalence relation.Find the set of all elements related to 1.

Prove that the relation R is the set A= {5,6,7,8,9,10} given by R= {(a, b) : |a - b| is divisible by 2} is an equivalence relation. Find the all elements related to the element 6.

Let R be the equivalence relation in the set Z of integers given by R={(a,b):2 divides a-b} .Write the equivalence class of [0]