Question

For each of the following sets. state with reasons whether it is a null set.
(i) A = {x|x $\in$ I x² is not positive}
(ii) B = {b|b $\in$ N, 2b + 1 is even}
(iii) C = {c|c $\in$ N, c is odd and c² is even}

Answer 1

We have to identify the null sets from the following sets:

(i) A = {0}
This is not a null set.
Reason: 0$\in$A and 0 is not positive

(ii) B = $\mathrm{\varphi }$
This is a null set.
Reason: If b belongs to a natural number, then 2b + 1 is always an odd number, not even.
Example: If b = 1, then 2b + 1 = 2 $\times$1 + 1 = 3
If b = 2, then 2b + 1 = 2 $\times$2 + 1 = 5
Hence, it will always be an odd number.

(iii) C = $\mathrm{\varphi }$
This is a null set.
Reason: The square of an odd natural number is always an odd number .