What are relations?. Types of Relations Class XII - maths chapter 1

 

What are relations?

 

Before explaining what the meaning of relations is, we’ll recall the meaning of cartesian product.

So if we have two sets

A = { a, b, c}

B = { x, y}

Then randomly we can associate each element of A with each element of B

So, Cartesian product is

A X B = { (a, x). (a, y), ( b, x ) ( b, y), (c, x) , (c, y)}

 

Now if we set a rule on the basis of which we associate each element of set A with element(s) of set B then that ordered pair will be called relation. Same thing we do in real life.

e.g.1 if a man gets married to a woman then that man will be called the husband of the woman. So , a man will be related to a woman with the relation of “ is a husband” if and only if he has married that woman.

Mr. Alex is husband of Mrs. Sophia since he married her

e.g.2 “Alphabets” of set A are related to “word(s)” of set B if the word starts with the letter selected from set A

We can write this relation as

R = { (a, apple), (b, ball), (b, box) , (c, cat), ( c, car) }

 

Generalizing the definition:

So, in simple words if element “a” of set A gets associated with element “b” of set B on the basis of a rule then we’ll say that “a” is related to “b”.

TYPES OF RELATIONS

 

Now, within a few seconds he again measured his weight and no surprises it is still 100 kg.

Is Mr. A related to himself with the above relation?

The answer is YES.

As in the statement : A is related to B if A’s weight is equal to B’s weight, where A and B are human beings.

If we replace B by A the statement makes sense and is meaningful

A is related to A if A’s weight is equal to A’s weight, where A and A are human beings.

So, If a relation is such that , that each and every element of the given set is related with itself then the relation will termed as Reflexive relation.

Now think , can A be 7 cm taller than himself?

The answer is NO.

No one can be taller than himself.

So A is not related to A in this case.

So in this case relation is not reflexive

Generalizing the definition:

So, in simple words if element “a” of set A is related to “a” for each and every “a” belongs to “a” then the relation is reflexive.

I guess already the blog is too long . Let us discuss the other two types of relations in the next blog. 

PART - 2 RELATIONS ( SYMMETRIC AND TRANSITIVE RELATIONS)

Keep studying maths and stay blessed.