Prove that r is an equivalence relation, Mathematics

Assignment Help:

1. Let S be the set of all nonzero real numbers. That is, S = R - {0}. Consider the relation R on S given by xRy iff xy > 0.

(a) Prove that R is an equivalence relation on S, and describe the distinct equivalence classes of R.

(b) Why is the relation R₂ on S given by xR₂y iff xy < 0 NOT an equivalence relation?

Related Discussions:- Prove that r is an equivalence relation

How many students are study physics alone, A class has 175 learners. The gi...

A class has 175 learners. The given table describes the number of learners studying one or more of the subsequent subjects in this case Subjects

If tana+sina=m and tana-sina=n, If tanA+sinA=m and tanA-sinA=n, show that m...

If tanA+sinA=m and tanA-sinA=n, show that m 2 -n 2 = 4√mn Ans: TanA + SinA = m TanA - SinA = n. m 2 -n 2 =4√mn . m 2 -n 2 = (TanA + SinA) 2 -(TanA - SinA) 2

Time=distance/speed, time=2.82/4000

time=2.82/4000

Minima, Minima, Maxima and points of inflexion a) Test for rela...

Minima, Maxima and points of inflexion a) Test for relative maximum Consider the given function of x whose graph is presented by the figure given below

Point-slope form, The next special form of the line which we have to look a...

The next special form of the line which we have to look at is the point-slope form of the line. This form is extremely useful for writing the equation of any line. If we know that

Prepare a bar diagram, Question Write a short note on the following: ...

Question Write a short note on the following: 1 The weekly salaries of a group of employees are given in the following table. Find the mean and standard deviation of the

Partial Differential Equation, Consider the wave equation u_tt - u_xx = 0 w...

Consider the wave equation u_tt - u_xx = 0 with u(x, 0) = f(x) = 1 if -1 Please provide me a detailed answer. I had worked the most part of this question and the only I would like

Union of sets, Union of Sets Venn diagram presenting the union of sets...

Union of Sets Venn diagram presenting the union of sets A and B or A?B = Shaded area is demonstrated below: A ?B = Shaded area

Important points about the alternating series test, Important Points About ...

Important Points About the Alternating Series Test There are a several things to note about this test. Very first, unlike the Integral Test and the Comparison or Limit Compari

Show that the ratio of the volume of the sphere, A sphere and a cube have e...

A sphere and a cube have equal surface areas. Show that the ratio of the volume of the sphere to that of the cube is √6 : √π. Ans: S.A. of sphere = S.A of cube 4π r 2

Write Your Message!

Name

Email id

Message

Verfication Code

User Account

All Pages