If A = {x : x ∈ ℕ and x is a prime number less than 2}, what kind of set is A?
Answer and explanation
Correct answer: Empty set
The smallest prime number is 2. Therefore, there is no prime number smaller than 2. The defining condition for A asks for a natural number that is simultaneously prime and less than 2, but no such number exists. Whenever no element satisfies the rule defining a set, the set has no members and is called the empty set. Hence A = ∅.
Frequently asked questions
What is the correct answer to this question?
Empty set
Why is this the correct answer?
The smallest prime number is 2. Therefore, there is no prime number smaller than 2. The defining condition for A asks for a natural number that is simultaneously prime and less than 2, but no such number exists. Whenever no element satisfies the rule defining a set, the set has no members and is called the empty set. Hence A = ∅.
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.
