Home
Class 11
MATHS
Let R be the set of all real numbers. Co...

Let R be the set of all real numbers. Consider the following subsets of the plane `RxxR: S={(x,y):y=x+1and0ltxlt2}andT={(x,y):x-y` is an integer}
Then which of the following is true?

A

T is an equivalence relation but S is not an equivalence relation.

B

Neither S nor T is an equivalence relation

C

Both S and T are equivalence relation

D

S is an equivalence relation but T is not an equivalence relation.

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • SAMPLE PAPER-07 (UNSOLVED)

    FULL MARKS|Exercise PART-II|10 Videos
  • SAMPLE PAPER-07 (UNSOLVED)

    FULL MARKS|Exercise PART-III|8 Videos
  • SAMPLE PAPER 16 (UNSOLVED

    FULL MARKS|Exercise PART-IV|7 Videos
  • SAMPLE PAPER-20 (MOCK TEST PAPER)

    FULL MARKS|Exercise PART-IV|5 Videos

Similar Questions

Explore conceptually related problems

Let RR be the set of all real numbers. Consider the following subsets of the plane RRxxRR :S = { (x,y) : y=x+1 and 0 lt x lt 2 } and T = { (x,y) : x-y is an integer }. Then which of the following is true ?

The relation R defined on a set A={0,-1,1,2} by xRy" if "|x^2+y^2| le 2 , then which one of the following is true?

Let N be the set of natural numbers and the relation R be defined on N such that R={(x,y): y=2x,x,y in N }. what is the domain codomain and range of R ? Is this relation a functions ?

Which of the following sets are equivalent? X={x:x inNN,1ltxlt6} , Y = {x : x is a vowel in the English Alphabet}

The relation R defined on a set A = { 0,-1,1,2} by xRy if | x^(2)+y^(2)| lt=2 , then which one of the following is true?

Consider the points O(0,0), A(0,1), and B(1,1) in the x-y plane. Suppose that points C(x,1) and D(1,y) are chosen such that 0ltxlt1. And such that O,C, and D are collinear. Let the sum of the area of triangles OAC and BCD be denoted by S. Then which of the following is/are correct?.

List all the elements of the following sets : B = {x : x is an integer, -(1)/(2)ltxlt(9)/(2) }