If \(A=\{x\in\mathbb{N}:x\le 30,\ x\text{ is a perfect square}\}\) and \(B=\{x\in\mathbb{N}:x\le 30,\ 3\mid x\}\), what is \(A-B\)?
Answer and explanation
Correct answer: \(\{1,4,16,25\}\)
The natural-number perfect squares not exceeding 30 are \(1,4,9,16,25\), so \(A=\{1,4,9,16,25\}\). The set \(B\) contains numbers up to 30 divisible by 3. Among the elements of \(A\), only 9 is divisible by 3, because \(9=3\times3\). Set difference \(A-B\) means retaining elements of \(A\) that are not in \(B\). Thus, \(A-B=\{1,4,16,25\}\), making option A correct.
Frequently asked questions
What is the correct answer to this question?
\(\{1,4,16,25\}\)
Why is this the correct answer?
The natural-number perfect squares not exceeding 30 are \(1,4,9,16,25\), so \(A=\{1,4,9,16,25\}\). The set \(B\) contains numbers up to 30 divisible by 3. Among the elements of \(A\), only 9 is divisible by 3, because \(9=3\times3\). Set difference \(A-B\) means retaining elements of \(A\) that are not in \(B\). Thus, \(A-B=\{1,4,16,25\}\), making option A correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
