Home
Class 11
MATHS
Let P be the set of all triangles in a p...

Let P be the set of all triangles in a plane and R be the relation defined on P as a Rb if a is similar to b. Prove that R is an equivalence relation .

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
Promotional Banner

Topper's Solved these Questions

  • SAMPLE PAPER 16 (UNSOLVED

    FULL MARKS|Exercise PART-III|10 Videos

  • SAMPLE PAPER 16 (UNSOLVED

    FULL MARKS|Exercise PART-IV|7 Videos

  • SAMPLE PAPER 16 (UNSOLVED

    FULL MARKS|Exercise PART-IV|7 Videos

  • SAMPLE PAPER 14

    FULL MARKS|Exercise PART - IV|8 Videos

  • SAMPLE PAPER-07 (UNSOLVED)

    FULL MARKS|Exercise PART-IV|7 Videos

Similar Questions

Explore conceptually related problems

In the set Z of integers, define m Rn if m-n is a multiple of 12. Prove that R is an equivalence relation.

In the set Z of integers, define mRn if m-n is divisible by 7. Prove that R is an equivalence relation.

In the set Z of integers define mRn if m-n is a multiple of 12 . Prove the R is an equivalence relation.

Let Z be the set of all integers and R be the relation on Z defined as R={(a , b); a ,\ b\ in Z , and (a-b) is divisible by 5.} . Prove that R is an equivalence relation.

In the set z of integers, define mRn if m-n is div7 , prove that R is an equivalence relation.

Prove that the relation R defined on the set V of all vectors by vecaRvecbif veca=vecb, is an equivalence relation on V.

Let L be the set of all lines in a plane and R be the relation in L defined as R = {(L _(1), L _(2)) : L _(1) is perpendicular to L _(2) }. Show that R is symmetric but neither reflexive nor transitive.

Prove that set of similar triangles, 'is similar to' is an equivalence relation