Let R : A⟶ B, R = {(a1, b1 ), (a2, b4 ), (a4, b1 ), (a3, b2 ), (a5, b3 )}. Is relation R a function and if is function

Question

In two different societies, there are some school going students including girls as well as boys. Satish forms two sets with these students for his college project.

Let = {a₁, a₂, a₃, a₄, a₅ } and B= {b₁, b₂, b₃, b₄ } where ai's and bi's are school going students of first and second societies respectively.

Satish decides to explore these sets for various types of relations and functions.

With the help of above information answer the following question:

Let R : A⟶ B, R = {(a₁, b₁ ), (a₂, b₄ ), (a₄, b₁ ), (a₃, b₂ ), (a₅, b₃ )}. Is relation R a function and if is function then what kind of function it ? Also find the domain of R.

Answer 1

Given relation R is R = {(a₁, b₁ ), (a₂, b₄ ), (a₄, b₁ ), (a₃, b₂ ), (a₅, b₃ )} and relation is defined from set A to set B.

Since, every element of set A has one and only one image under the relation R, therefore, relation R is a function. (By definition of the function)

Now, domain of function R is {a₁, a₂, a₃, a₄, a₅ } = A

Range of function R is {b₁, b₂, b₃, b₄ } = B = codomain of function R.

Therefore, R is onto function.

But, R(a₁ ) = R(a₄ ) = b₁.

Therefore, R is not one-one function.

Hence, R is onto but not one-one function.