Properties of relations in a set, Mathematics

Assignment Help:

Reflexive Relations:

R is a reflexive relation if (a, a) € R,  a € A. It could be noticed if there is at least one member a € A like (a, a) € R, then R is not reflexive.

Symmetric Relations:

R is called a symmetric relation on A if (x, y)€ R →(y, x) € R

That is, y R x when x R y.

It could be noticed that R is symmetric iff R-1 = R

Assume A = {1, 2, 3}, then R = {(1, 1), (1, 3), (3, 1)} is symmetric.

 

Anti-symmetric Relations:

R is called as a anti-symmetric relation if (a, b) €R  and  (b, a)  €R →a = b

Thus, if a  € b then a can be belongs to b or b can be belongs to a, but never both.

Or, we have never both a R b and b R a apart from when a = b.

 


Related Discussions:- Properties of relations in a set

Polynomials, sum of zero of polynomial x2-2x+1is equal to sum of zero of po...

sum of zero of polynomial x2-2x+1is equal to sum of zero of polynomial x3-2x+x then find the product of all the three zero of the second polynomial

Mean and standard deviation, Q. Mean and Standard Deviation? Ans. ...

Q. Mean and Standard Deviation? Ans. The normal distribution is totally described if we know the average and standard deviation. - the population mean of the distribu

Find out that vector are linearly dependent, Find out if the following set ...

Find out if the following set of vectors are linearly independent or linearly dependent. If they are linearly dependent get the relationship among them. Solution : Ther

Trigonomitry, Ask if tanA+sinA=m and m^2-n^2=4 rute mn show that tanA-sinA=...

Ask if tanA+sinA=m and m^2-n^2=4 rute mn show that tanA-sinA=n

Reason why we start division, Reasons why we start division : The reason w...

Reasons why we start division : The reason we start division by considering the digit in the leftmost place is efficiency and ease . For instance, suppose we divide 417 by 3, we

Las leyes de kepler, la expresión que permite calcular el radio medio de la...

la expresión que permite calcular el radio medio de la órbita de cada planeta es?

Finding the LCM, what is the LCM of 18, 56 and 104 show working

what is the LCM of 18, 56 and 104 show working

Range of f(x) =4^x+2^x+1 is, Taking 2^x=m and solving the quadratic for get...

Taking 2^x=m and solving the quadratic for getting D>=0 we get range= [3/4 , infinity )

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