What type of set is A = {x ∈ ℕ : x is both prime and composite}?
Answer and explanation
Correct answer: Empty set
A prime number has exactly two positive factors: 1 and itself. A composite number has more than two positive factors. These definitions are mutually exclusive, so no natural number can be both prime and composite. Since no element satisfies the defining condition, the set contains no elements and is therefore the empty set.
Frequently asked questions
What is the correct answer to this question?
Empty set
Why is this the correct answer?
A prime number has exactly two positive factors: 1 and itself. A composite number has more than two positive factors. These definitions are mutually exclusive, so no natural number can be both prime and composite. Since no element satisfies the defining condition, the set contains no elements and is therefore the empty set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
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