Question 1: Give an example  of a function

(i) which is one-one but not onto

(ii) which is not one-one but onto

(iii) which is neither one-one nor onto

Answer:

(i)     

Check for Injectivity:

Check for Surjectivity:

Check for Injectivity:

So, from definition

Check for Surjectivity:

(iii) which is neither one-one nor onto

Question 2:  Which of the following functions from A to B are one-one and onto?

Answer:

(i) Now, As given,

Thus we can see that,

Check for Injectivity:

Every Element of has a different image from

Hence is a One – One function

Check for Surjectivity:

Also, each element of is an image of some element of

Hence is Onto.

(ii) Now, As given,

Thus we can see that

Check for Injectivity:

Every element of has a different image from

Hence is a One – One function

Check for Surjectivity:

Also, each element of is an image of some element of

Hence is Onto.

(iii) Now, As given,

Thus we can clearly see that

Check for Injectivity:

Every element of does not have different image from

Therefore is not One – One function

Check for Surjectivity:

Also each element of is not image of any element of

Hence is not Onto.

Answer:

Check for Injectivity:

So, from definition

Check for Surjectivity:

Answer:

Check for Injectivity:

Check for Surjectivity:

Question 5: Classify the following functions as injection, surjection or bijection:

Answer: 

Injection condition:

Surjection condition:

Injection condition:

Surjection test:

Injection condition:

Surjection condition:

Injection condition:

Surjection condition:

Injection condition:

Surjection test:

Injection test:

Surjection test: