Answer to Question #154238 in Discrete Mathematics for Hello

Question

He relation (a,b) such that "a" and "b" have the same age ,is defined on the sets of all people.Is it equivalent relation?

Answer 1

To show that (a,b) is an equivalent relation we have to prove 3 properties:

1) Reflexivity: for all a the object a has the same age as a. (It's evident)

2) Symmetry: if a has the same age as b, then b has the same age as a. (It's evident)

3) Transitivity: if a has the same age as b, and b has the same age as c, then a has the same age as c.

Let x be an age of a. As the age of b is the same as the age of a, it's equal to x too.

As the age of c is the same as the age of b, it's equal to x also.

Then the ages of a and c both equal to x, and, hence, are the same.

Thus, (a,b) is an equivalent relation.