We define a relation on set of Whole Numbers
W={0,1,2,3…} As follows:
We divide the number by 5 and look at the remainder. All numbers that result into the same
remainder are related.
E.g. 2/5 remainder =2, 7/5 remainder =2 and 12/5 remainder =2, therefore 2R7, 7R2, 7R12,
12R7, 12R2, and 2R12 etc.
[2] = {2,7,12,17….}
How many Equivalence classes are there.
Write the first four members of each equivalence class
Solution
Given whole number set {0,1,2,3........}
The numbers divides by 5
Any number divided by 5 we get 0,1,2,3,4 are only the remainders.
The number which is exactly divisble by 5 we get remainder 0.
The number which is not divisible by 5 we get the remainders(1,2,3or4).
Since the given set is a whole numbers set ..the divisble numbers of 5 are greater than five and
5.that mean the whole numbers from5,6,7....are divisible by 5.
There are five equivalence classes for 5.
The frist four members of each equivalence is
[0]={0,5,10,15...}
[1]={1,6,11,16......}
[2]={2,7,12,17......]
[3]={3,8,13,18.......}
[4]={4,9,14,19.......}.
For zero remainder
5/5=0,10/5=0,….
Therefore{0,5,10,15.....}
For 1
6/5=1,11/5=1...
For2
7/5=2,12/5=2,...
For 3
8/5=3,13/5=3.....
For 4
9/5=4,14/5=4,......
Simple, Complex, and Compound Sentences Exercises.pdf
We define a relation on set of Whole NumbersW={0,1,2,3…} As follow.pdf
1. We define a relation on set of Whole Numbers
W={0,1,2,3…} As follows:
We divide the number by 5 and look at the remainder. All numbers that result into the same
remainder are related.
E.g. 2/5 remainder =2, 7/5 remainder =2 and 12/5 remainder =2, therefore 2R7, 7R2, 7R12,
12R7, 12R2, and 2R12 etc.
[2] = {2,7,12,17….}
How many Equivalence classes are there.
Write the first four members of each equivalence class
Solution
Given whole number set {0,1,2,3........}
The numbers divides by 5
Any number divided by 5 we get 0,1,2,3,4 are only the remainders.
The number which is exactly divisble by 5 we get remainder 0.
The number which is not divisible by 5 we get the remainders(1,2,3or4).
Since the given set is a whole numbers set ..the divisble numbers of 5 are greater than five and
5.that mean the whole numbers from5,6,7....are divisible by 5.
There are five equivalence classes for 5.
The frist four members of each equivalence is
[0]={0,5,10,15...}
[1]={1,6,11,16......}
[2]={2,7,12,17......]
[3]={3,8,13,18.......}
[4]={4,9,14,19.......}.
For zero remainder
5/5=0,10/5=0,….
Therefore{0,5,10,15.....}
For 1
6/5=1,11/5=1...
For2
7/5=2,12/5=2,...
For 3
8/5=3,13/5=3.....
![We define a relation on set of Whole Numbers
W={0,1,2,3…} As follows:
We divide the number by 5 and look at the remainder. All numbers that result into the same
remainder are related.
E.g. 2/5 remainder =2, 7/5 remainder =2 and 12/5 remainder =2, therefore 2R7, 7R2, 7R12,
12R7, 12R2, and 2R12 etc.
[2] = {2,7,12,17….}
How many Equivalence classes are there.
Write the first four members of each equivalence class
Solution
Given whole number set {0,1,2,3........}
The numbers divides by 5
Any number divided by 5 we get 0,1,2,3,4 are only the remainders.
The number which is exactly divisble by 5 we get remainder 0.
The number which is not divisible by 5 we get the remainders(1,2,3or4).
Since the given set is a whole numbers set ..the divisble numbers of 5 are greater than five and
5.that mean the whole numbers from5,6,7....are divisible by 5.
There are five equivalence classes for 5.
The frist four members of each equivalence is
[0]={0,5,10,15...}
[1]={1,6,11,16......}
[2]={2,7,12,17......]
[3]={3,8,13,18.......}
[4]={4,9,14,19.......}.
For zero remainder
5/5=0,10/5=0,….
Therefore{0,5,10,15.....}
For 1
6/5=1,11/5=1...
For2
7/5=2,12/5=2,...
For 3
8/5=3,13/5=3.....](https://image.slidesharecdn.com/wedefinearelationonsetofwholenumbersw0123asfollow-230711202615-85bf289a/85/We-define-a-relation-on-set-of-Whole-NumbersW-0-1-2-3-As-follow-pdf-1-320.jpg)
