Question

Let J be the collection of natural numbers defined by the following recursion:

(a) 0 ∈ J.

(b) If n ∈ J, then both n + 2 and 3n belong to J.

Which natural numbers less than 40 belong to J

Answer 1

Assuming n belongs to set of all integers,

It says that J is a collection of natural numbers. Now natural numbers comprise of all positive integers i.e. 1,2,3,.......n

Now, (a) says that 0 belongs to J, so its a special case as 0 doesn't belong to a set of natural numbers yet the recursion defines it so we will consider it.

From (b), we can observe that if we take, n=1, we get 1+2 = 3 as well as 1*2 = 2

Similarly, for n = 2, we get 2+2 = 4 as well as 2*3 = 6

For, n = 3, we get 3+2 = 5 as well as 3*2 = 6....

Going by the pattern, we see that all the positive integers less than 40 and 0 belong to J

So, J = {0, 1, 2, 3.........39}