Each of the following defines a relation on N: x y is square of an integer x, y ∈ N Determine whether above relation is reflexive, symmetric and transitive.

Question

Harshit Singh · Answer

Dear Student

Given, xy is square of an integer x, y∈N

R = {(x, y) : xy is a square of an integer x, y∈N}

It’s clearly (x, x)∈R,∀x∈N

As x^2is square of an integer for any x∈N

Thus, R is reflexive.

If (x, y)∈R⇒(y, x)∈R

So, R is symmetric.

Now, if xy is square of an integer and yz is square of an integer.

Then,let xy=m^2and yz= n^2for some m,n∈Z

x = m^2/y and z = x^2/y

xz = m^2 n^2 / y^2 , which is square of an integer.

Thus, R is transitive.

Thanks

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

Each of the following defines a relation on N: x y is square of an integer x, y ∈ N Determine whether above relation is reflexive, symmetric and transitive.

Each of the following defines a relation on N:
x y is square of an integer x, y ∈ N

Determine whether above relation is reflexive, symmetric and transitive.

1 Answers

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

Other Related Questions on Magical Mathematics[Interesting Approach]

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship