Question

Given that $N = \\{ 1,2,3......100\\}$ then write
i) The subset of N whose elements are even numbers.
ii) The subset of N whose elements are perfect square numbers.

Answer 1

As we know that all elements of the subset are from elements of the set $N$. So we will find out even numbers and perfect square numbers from the elements of the set $N$ as the given set $N$ belongs to the number system from 1 to 100.

Complete step by step solution:
i) The subset of $N$ whose elements are even numbers will be the even numbers present in the set $N$. First of all we will observe that set $N$ contains all numbers 1 to 100, so we will find out the even numbers present between 1 to 100.
As we know that the number which is divisible by 2 and leaves remainder 0 is an even number. So 2, 4, 6, 8… 100 are the even numbers between 1 to 100. We can write the subset of even numbers present in the set as below:
Subset of $N = \\{ 2,4,6......100\\}$

ii) The subset of $N$ whose elements are perfect square numbers will be perfect squares between 1 to 100 as the number presents in the set are 1 to 100. As we know that a perfect square is a number that can be expressed as the square of a number. So 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 are perfect square numbers present in the set. We can write the subset of perfect square numbers present in the set as below:
Subset of $N = \\{ 1,{{ }}4,{{ }}9,{{ }}16,{{ }}25,{{ }}36,{{ }}49,{{ }}64,{{ }}81,100\\}$

Note:
We should know that the number which is divisible by 2 and leaves remainder 0 is an even number and a perfect square is a number in a number system that can be expressed as the square of a number in that number system.