If A = {x : x is a perfect-square natural number less than 4}, what is A?
Answer and explanation
Correct answer: A = {1}
A perfect-square natural number is a natural number that can be written as the square of a natural number. The natural numbers less than 4 are 1, 2, and 3. Of these, only 1 is a perfect square because 1 = 1². Although 4 = 2², it is not included because the condition is strictly less than 4. Therefore A = {1}, so option A is correct; the other options either include excluded numbers or wrongly make the set empty.
Frequently asked questions
What is the correct answer to this question?
A = {1}
Why is this the correct answer?
A perfect-square natural number is a natural number that can be written as the square of a natural number. The natural numbers less than 4 are 1, 2, and 3. Of these, only 1 is a perfect square because 1 = 1². Although 4 = 2², it is not included because the condition is strictly less than 4. Therefore A = {1}, so option A is correct; the other options either include excluded numbers or wrongly make the set empty.
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.
