Mock Test : Q. 11 - 13. Please Explain

[Akshay Malik]

Just help me with the finding the three sets.

[DHARMA TEJA GODUMALA]

[Akshay Malik]

Yeah! Got it. I had been constantly putting f(0) = 0 in all the calculations.

[Mohamed Juned Khan]

How the value of T is calculated as 3?Can you show steps please?

[Mathematics 1 Support 2]

Hi,

If you see properly you can get that T is the set defined by-product of two numbers such as (n-1)*(some other number).

For example, take A = m*n. Then A is the number which is a product of two numbers so it can not be prime until unless one number (either a or b) is a prime number and another number must be 1. 
 This case you will get when you put n=1 in set T.

Hope it will clear your doubt. 

Bests,

Rahul

[Srinath Sai]

Question 13: 

I didn't understand why in the Mock Test Solutions Pdf given for this Question 13, the reason for the function not being surjective is given as 'There is no value in the domain for which it gives 3 as the output value'. 

I have understood the reason to be: the Range having only a few natural numbers {0, 1, 2, 9, 44, 265}, is definitely not equal to the Co-domain which has all the Natural numbers.  

Kindly clarify. Thank you.

 

[subhajit POD]

Hi Srinath, 

A function is not onto if the range of the function is not same as the codomain. Here the codomain is the set of natural numbers.  So 3 is in the codomain which is not in the range. Yes, certainly there are many such natrual numbers which are not in the range as you can see. But it is enough to find atleast one. That is why the example of 3 is given. 

Hope it clarifies your doubt. 

Best

Subhajit

[Srinath Sai]

Thank you!