Question

Which of the following statements is false? (N = natural numbers)

Ø N
{0} N
{1} N

Answer 1

Assuming each statement is claiming the first set is a subset of N, the second statement is false. 0 is not part of the natural numbers.

Answer 2

Option 2 -
`\{0\}\in N`

Explanation:

Given : N = Natural numbers

To find : Which of the following statements is false?

Solution :

The natural numbers is the set of positive integers which is {1,2,3,4,5,6,7,8,9}.

1)
`\phi \in N`

This statement is true as
`\phi` is an empty set exist in every set.

2)
`\{0\}\in N`

This statement is false as natural number starts from 1.

3)
`\{1\}\in N`

This statement is true as natural number starts from 1.

Therefore, the false statements is
`\{0\}\in N`

So, option 2 is correct.