If S = {x : x ∈ N, x is a prime number less than 50, and x is even}, what is S?
Answer and explanation
Correct answer: S = {2}
A prime number has exactly two positive divisors: 1 and itself. The only even prime number is 2; every other even natural number is divisible by 2 and therefore has at least one additional divisor, so it is composite. Since 2 is less than 50, it satisfies both conditions. Thus S = {2}, a singleton set containing one element.
Frequently asked questions
What is the correct answer to this question?
S = {2}
Why is this the correct answer?
A prime number has exactly two positive divisors: 1 and itself. The only even prime number is 2; every other even natural number is divisible by 2 and therefore has at least one additional divisor, so it is composite. Since 2 is less than 50, it satisfies both conditions. Thus S = {2}, a singleton set containing one element.
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.
