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

What was the total cost of the copies, Mary made 34 copies at the local off...

Mary made 34 copies at the local office supply store. The copies cost $0.06 each. What was the total cost of the copies? Multiply 34 by $0.06 to ?nd out the total cost; 34 × $0

Discrete, For each of these arguments determine whether the argument is cor...

For each of these arguments determine whether the argument is correct or incorrect and explain why. a) Everyone enrolled in the university has lived in a dormitory. Mia has never l

How to convert decimals to fractions, Q. How to Convert decimals to fractio...

Q. How to Convert decimals to fractions? Ans. Note: This tutorial covers only terminating decimals.

Sketch the parametric curve for parametric equations, Sketch (draw) the par...

Sketch (draw) the parametric curve for the subsequent set of parametric equations. x = t 2 + t y = 2t -1 Solution At this point our simply option for sketching a par

Determine the size of belt, On a piece of machinery, the centers of two pul...

On a piece of machinery, the centers of two pulleys are 3 feet apart, and the radius of each pulley is 6 inches. Determine the size of belt (in feet) is required to wrap around bot

Example of negative number, Q. Example of negative number? If you take ...

Q. Example of negative number? If you take an elevator 8 stories  down , what would be the opposite of this? The opposite would be that you take the elevator 8 stories  up .

Find the number of students side of the square, A teacher on attempting to ...

A teacher on attempting to arrange the students for mass drill in the form of a solid square found that 24 students were left over. When he increased the size of the square by one

Calculus, I need help with my calculus

I need help with my calculus

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd