Question

Good morning early birds
Class 12th
Chapter 1st
Relation and function
example 5



I want to know how do you get 'c'
when c is not given in question


and why 'b-c is divisible by 2'
and 'a-c is divisible by 2'


even if c is some arbitrary number
what if it is odd or even or prime number

why this can be transitive

give the answer n you r brainliest​

Answer 1

Step-by-step explanation:

There's a relation given, expressed in terms of some variables.

Let's write the relation first :

R = { (a,b) : 2 divides a-b}

Did u understand this relation ?

It means that a and b are related to each other such that difference of them will be divisble by 2.

So, you can take those values of a and b only if they satisfy the given relation.

Now, in the solution it has been taken a new variable 'c' and u got tempted, right ?

Don't Worry, that's just a variable, and variable can be anything from a,b,c.....z.

Now, in order to find equivalence relation.

You need to prove all th three relations :

• Reflexive - Variable Related to itself
• Symmetric - If a related b then b must be related to a also.
• Transitive - If aRb and bRc, then aRc.

So, in order to prove that, transitive relation, a new variable 'c' was needed to be taken.

Now, if aRb then (a-b) is divisible by 2 as it is given relation.

Similarly, if bRc , then According to the given relation, (b-c) is divisible.

Now, if aRb and bRc , then bRc also.

Therefore, (b-c) is divisible by 2.

You can further verify all these by taking random constants and satisfying the Given relation.

Answer 2

what is this all you typed