Let R be the real line. Consider the following subsets of the plane R andtimes; R:S ={(x, y): y = x + 1 and 0 andlt; x andlt; 2}T ={(x, y): x andndash; y is an integer},Which one of the following is true? [2008]a)Neither S nor T is an equivalence relation on Rb)Both S and T are equivalence relation on Rc)S is an equivalence relation on R but T is notd)T is an equivalence relation on R but S is notCorrect answer is option 'D'. Can you explain this answer?

Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity

Open App

JEE Exam > JEE Questions > Let R be the real line. Consider the followin...

Join the Discussion on the App

Let R be the real line. Consider the following subsets of the plane R × R:
S ={(x, y): y = x + 1 and 0 < x < 2}
T ={(x, y): x – y is an integer},
Which one of the following is true? [2008]

a)
Neither S nor T is an equivalence relation on R
b)
Both S and T are equivalence relation on R
c)
S is an equivalence relation on R but T is not
d)
T is an equivalence relation on R but S is not

Correct answer is option 'D'. Can you explain this answer?

FREE This question is part of

Test: JEE Main 35 Year PYQs- Complex Numbers

Attempt Test

Attempt this Test

Verified Answer

Let R be the real line. Consider the following subsets of the plane R ...

Given S = {(x , y) : y = x + 1 and 0 < x < 2}
∵ x ≠ x + 1 for any x ∈(0, 2) ⇒ (x, x) ∉ S
∴ S is not reflexive.
Hence S in not an equivalence relation.
Also T ={x, y): x – y is an integer}
∵ x – x = 0 is an integer " x ∈ R
∴ T is reflexive.
If x – y is an integer then y – x is also an integer
∴T is symmetric If x – y is an integer and y – z is an integer then (x – y) + (y– z) = x – z is also an integer.
∴ T is transitive Hence T is an equivalence relation.

View all questions of this test

View all answers Start learning for free

< Previous Question Next Question >

Explore Courses for JEE exam

Similar JEE Doubts

Consider the following relations: R = {(x, y) | x, y are real numbers and x = wy for some rational number w};and q are integers such that n, q ≠ 0 and qm = pn}.Then [2010]

View answer

Which of the following is not an equivalence relation on I, the set of integers ; x, y

View answer

Volumetric analysis is based on the principle of equivalence a that minloces lead in the ratio of their equivalents. At the equivalence point of the reaction, involving the reactahts A and B : Number of gram equivalents of A = Number of gram equivalents of B..If VA ml of solution A having normality NA react just completely with VB ml of solution B having normalityNB thenEquation(1), called normality equation is very useful in numerical of volumetric analysis. Equivalent masses of different substances :Basically the equivalent mass of a substance is defined as the pads by seam ctituhich combine with or displace 1.0078 parts (1part) by mass of hydrogen, 8 parts by mansetaisiosaid 35.5 parts by mass of chlorine.Mass of a substance expressed in gram equal to its equivalent man is gam equivalent mass. Equivalent mass of a substance is not constant but depends upon the maw i malice the substance participates.Equivalent mass of an acid in acid-base reaction is its mass in grannehidicodoinisooleaf replaceable Fi ions (= 1.0078 g1g).0n the other hand, equivalent mass of a bagels istolonellfacontairis 1 mole of replaceable 0H ions. 1 g equivalent mass each of an acid and base an ionclinegins saint and 1 mole of water= 18 g). Equivalent mass of an oxidising agent is its mass which gains 1 mole at ellecismitcan be obtained by dividing the molecular mass or formula mass by the total decrease in aididditaiiilberef one or more elements per molecule.0n the other hand, equivalent mass of a reducing agent is the mass of the substance which loses 1 mole of electorns. It can be calculated by dividing the molecular or formula mass of the subtance by the total increase in oxidation number of one or more elements per molecular or formula mass.Q.Which of the following solutions, when mixed with 100 ml of 0.05 M NaOH, will give a neutral solution?

View answer

Volumetric analysis is based on the principle of equivalence a that minloces lead in the ratio of their equivalents. At the equivalence point of the reaction, involving the reactahts A and B : Number of gram equivalents of A = Number of gram equivalents of B..If VA ml of solution A having normality NA react just completely with VB ml of solution B having normalityNB thenEquation(1), called normality equation is very useful in numerical of volumetric analysis. Equivalent masses of different substances :Basically the equivalent mass of a substance is defined as the pads by seam ctituhich combine with or displace 1.0078 parts (1part) by mass of hydrogen, 8 parts by mansetaisiosaid 35.5 parts by mass of chlorine.Mass of a substance expressed in gram equal to its equivalent man is gam equivalent mass. Equivalent mass of a substance is not constant but depends upon the maw i malice the substance participates.Equivalent mass of an acid in acid-base reaction is its mass in grannehidicodoinisooleaf replaceable Fi ions (= 1.0078 g1g).0n the other hand, equivalent mass of a bagels istolonellfacontairis 1 mole of replaceable 0H ions. 1 g equivalent mass each of an acid and base an ionclinegins saint and 1 mole of water= 18 g). Equivalent mass of an oxidising agent is its mass which gains 1 mole at ellecismitcan be obtained by dividing the molecular mass or formula mass by the total decrease in aididditaiiilberef one or more elements per molecule.0n the other hand, equivalent mass of a reducing agent is the mass of the substance which loses 1 mole of electorns. It can be calculated by dividing the molecular or formula mass of the subtance by the total increase in oxidation number of one or more elements per molecular or formula mass.Q.100 ml of 0.1 M H3 P02 is titrated with 0.1 M NaOH. The volume of NaOH needed will be

View answer

Volumetric analysis is based on the principle of equivalence a that minloces lead in the ratio of their equivalents. At the equivalence point of the reaction, involving the reactahts A and B : Number of gram equivalents of A = Number of gram equivalents of B..If VA ml of solution A having normality NA react just completely with VB ml of solution B having normalityNB thenEquation(1), called normality equation is very useful in numerical of volumetric analysis. Equivalent masses of different substances :Basically the equivalent mass of a substance is defined as the pads by seam ctituhich combine with or displace 1.0078 parts (1part) by mass of hydrogen, 8 parts by mansetaisiosaid 35.5 parts by mass of chlorine.Mass of a substance expressed in gram equal to its equivalent man is gam equivalent mass. Equivalent mass of a substance is not constant but depends upon the maw i malice the substance participates.Equivalent mass of an acid in acid-base reaction is its mass in grannehidicodoinisooleaf replaceable Fi ions (= 1.0078 g1g).0n the other hand, equivalent mass of a bagels istolonellfacontairis 1 mole of replaceable 0H ions. 1 g equivalent mass each of an acid and base an ionclinegins saint and 1 mole of water= 18 g). Equivalent mass of an oxidising agent is its mass which gains 1 mole at ellecismitcan be obtained by dividing the molecular mass or formula mass by the total decrease in aididditaiiilberef one or more elements per molecule.0n the other hand, equivalent mass of a reducing agent is the mass of the substance which loses 1 mole of electorns. It can be calculated by dividing the molecular or formula mass of the subtance by the total increase in oxidation number of one or more elements per molecular or formula mass.Q.How many gram of phosphoric acid (H3PO4) would be required to neutralize 58 g of magnesium hydroxide?

View answer

Top Courses for JEEView all

Physics for JEE Main & Advanced

Mock Tests for JEE Main and Advanced 2025

Chemistry for JEE Main & Advanced

Mathematics (Maths) for JEE Main & Advanced

Chapter-wise Tests for JEE Main & Advanced

Top Courses for JEE

View all

Let R be the real line. Consider the following subsets of the plane R × R:S ={(x, y): y = x + 1 and 0 < x < 2}T ={(x, y): x – y is an integer},Which one of the following is true? [2008]a)Neither S nor T is an equivalence relation on Rb)Both S and T are equivalence relation on Rc)S is an equivalence relation on R but T is notd)T is an equivalence relation on R but S is notCorrect answer is option 'D'. Can you explain this answer?

Share with a Friend

Answer this doubt

Question Description
Let R be the real line. Consider the following subsets of the plane R × R:S ={(x, y): y = x + 1 and 0 < x < 2}T ={(x, y): x – y is an integer},Which one of the following is true? [2008]a)Neither S nor T is an equivalence relation on Rb)Both S and T are equivalence relation on Rc)S is an equivalence relation on R but T is notd)T is an equivalence relation on R but S is notCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let R be the real line. Consider the following subsets of the plane R × R:S ={(x, y): y = x + 1 and 0 < x < 2}T ={(x, y): x – y is an integer},Which one of the following is true? [2008]a)Neither S nor T is an equivalence relation on Rb)Both S and T are equivalence relation on Rc)S is an equivalence relation on R but T is notd)T is an equivalence relation on R but S is notCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let R be the real line. Consider the following subsets of the plane R × R:S ={(x, y): y = x + 1 and 0 < x < 2}T ={(x, y): x – y is an integer},Which one of the following is true? [2008]a)Neither S nor T is an equivalence relation on Rb)Both S and T are equivalence relation on Rc)S is an equivalence relation on R but T is notd)T is an equivalence relation on R but S is notCorrect answer is option 'D'. Can you explain this answer?.

Solutions for Let R be the real line. Consider the following subsets of the plane R × R:S ={(x, y): y = x + 1 and 0 < x < 2}T ={(x, y): x – y is an integer},Which one of the following is true? [2008]a)Neither S nor T is an equivalence relation on Rb)Both S and T are equivalence relation on Rc)S is an equivalence relation on R but T is notd)T is an equivalence relation on R but S is notCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.

Here you can find the meaning of Let R be the real line. Consider the following subsets of the plane R × R:S ={(x, y): y = x + 1 and 0 < x < 2}T ={(x, y): x – y is an integer},Which one of the following is true? [2008]a)Neither S nor T is an equivalence relation on Rb)Both S and T are equivalence relation on Rc)S is an equivalence relation on R but T is notd)T is an equivalence relation on R but S is notCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Let R be the real line. Consider the following subsets of the plane R × R:S ={(x, y): y = x + 1 and 0 < x < 2}T ={(x, y): x – y is an integer},Which one of the following is true? [2008]a)Neither S nor T is an equivalence relation on Rb)Both S and T are equivalence relation on Rc)S is an equivalence relation on R but T is notd)T is an equivalence relation on R but S is notCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Let R be the real line. Consider the following subsets of the plane R × R:S ={(x, y): y = x + 1 and 0 < x < 2}T ={(x, y): x – y is an integer},Which one of the following is true? [2008]a)Neither S nor T is an equivalence relation on Rb)Both S and T are equivalence relation on Rc)S is an equivalence relation on R but T is notd)T is an equivalence relation on R but S is notCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Let R be the real line. Consider the following subsets of the plane R × R:S ={(x, y): y = x + 1 and 0 < x < 2}T ={(x, y): x – y is an integer},Which one of the following is true? [2008]a)Neither S nor T is an equivalence relation on Rb)Both S and T are equivalence relation on Rc)S is an equivalence relation on R but T is notd)T is an equivalence relation on R but S is notCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Let R be the real line. Consider the following subsets of the plane R × R:S ={(x, y): y = x + 1 and 0 < x < 2}T ={(x, y): x – y is an integer},Which one of the following is true? [2008]a)Neither S nor T is an equivalence relation on Rb)Both S and T are equivalence relation on Rc)S is an equivalence relation on R but T is notd)T is an equivalence relation on R but S is notCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.

Explore Courses for JEE exam