Consider the following statements:

1. The null set is a subset of every set.

2. Every set is a subset of itself.

3. If a set has 10 elements, then its power set will have 1024 elements.

Which of the above statements are correct?

Concept:

1. The null set is a subset of every set. (ϕ ⊆ A)

2. Every set is a subset of itself. (A ⊆ A)

3. The number of subsets of a set with n elements is 2ⁿ.

Explanation:

1. The null set is a subset of every set - The intersection of two sets is a subset of each of the original sets.

So if {} is the empty set and A is any set then {} intersect A is {} which means {} is a subset of A and {} is a subset of {}.

You can prove it by contradiction. Let's say that you have the empty set {} and a set A.

2. Every set is a subset of itself. (A ⊆ A)

3. If n = 10 then  2¹⁰ = 1024

So, all three statements are true.