R is defined on A as follows

Question

A={ -4 ,-3 ,-2 ,-1 ,0 ,1 ,2 ,3 ,4} R is defined on A as follows: For All (m,n) ∈A,m R n ⇔ 5 | (m^2- n^2 )

Answer 1

The relation R defined on set

A={−4,−3,−2,−1,0,1,2,3,4}

is such that for all (m,n) in A,

mRn if and only if 55 divides (m2−n2).

In other words, for any pair (m,n) where m and n are elements of A,

the relation R holds true if(m2−n2) is divisible by 55.

Let's verify this relation for all possible pairs in A:

1. (−4,−4): (−4)2−(−4)2=0 which is divisible by 55. So, −4R−4.
2. (−4,−3): (−4)2−(−3)2=7 which is not divisible by 55. So,−4\nR−3.
3. (−4,−2): (−4)2−(−2)2=12 which is not divisible by 55. So, −4\nR−2.
4. (−4,−1): (−4)2−(−1)2=15 which is divisible by 55. So, −4R−1.
5. (−4,0): (−4)2−02=16 which is not divisible by 55. So, −4\nR0

Continuing this process for all pairs in A, we can determine the complete relation R according to the given condition.