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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?

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? Correct Answer 1, 2 and 3

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.

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