Question
Download Solution PDFConsider 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
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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