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

Repeated roots, Under this section we will be looking at the previous case ...

Under this section we will be looking at the previous case for the constant coefficient and linear and homogeneous second order differential equations. In this case we need soluti

Mechanical vibrations, While we first looked at mechanical vibrations we lo...

While we first looked at mechanical vibrations we looked at a particular mass hanging on a spring with the possibility of both a damper or/and external force acting upon the mass.

Prove that its inclination theta to the horizontal, Two stations due south ...

Two stations due south of a tower, which leans towards north are at distances 'a' and 'b' from its foot. If α and β be the elevations of the top of the tower from the situation, Pr

Twelve coworkers go out how many slices will each person get, Twelve cowork...

Twelve coworkers go out for lunch together and sequence three pizzas. Each pizza is cut within eight slices. If each person gets the similar number of slices, how many slices will

Example of multiplying decimals, Example of Multiplying Decimals: Exa...

Example of Multiplying Decimals: Example: 0.45 x 10 = 4.5. Same, while multiplying a decimal through 100, 1000, and 10,000, move the decimal point to the right the similar

Prove that sec2+cosec2 can never be less than 2, Prove that sec 2 θ+cosec 2...

Prove that sec 2 θ+cosec 2 θ can never be less than 2. Ans: S.T Sec 2 θ + Cosec 2 θ can never be less than 2. If possible let it be less than 2. 1 + Tan 2 θ + 1 + Cot

Solve simultaneous equations by graphical method, Solve the following pairs...

Solve the following pairs of simultaneous equations by elimination method i.2x+y=10 ii. 3x+y=6 3x-2y=1 5x+y=8 solve the following simult

#title.square footage, The area of a rectangular yard is 480 square feet. T...

The area of a rectangular yard is 480 square feet. The yard is 24 feet wide. How many feet do I need to fence all four sides?

Geometry, need answers

need answers

Equivalent fractions, what is 6/36 as two equivalent fractions 2/12 as tw...

what is 6/36 as two equivalent fractions 2/12 as two equivalent fractions 4/28 3/21 2/11 4/13=8/x 12/30=n/90 q/54=2/9 3/7 14/h=7/20

Write Your Message!

Name

Email id

Message

Verfication Code

User Account

All Pages