Question

Which of the following statements is/are true:

I. If A is a set then ϕ is a subset of A

II. If B = {x ∈ N : x < 1} then B is an empty set

1. Only I 
2. Only II
3. Both I and II
4. Neither I nor II

Answer 1

Correct Answer - Option 3 : Both I and II

Concept:

Null Set: A set which does not contain any element is called a null set. It is denoted by ϕ or {}

Note: ϕ is always a subset of any set

Calculation:

Statement I: If A is a set then ϕ is a subset of A

As we know that ϕ is always a subset of any set

So, statement I is true.

Statement II: If B = {x ∈ N : x < 1} then B is an empty set

As we know that if x ∈ N then x can never be less than 1

⇒ B = ϕ 

So, statement II is also true.

Hence, option 3 is the correct answer.