If \(A=\{x:x\in\mathbb{N},\ x\le 15,\ x\text{ is composite}\}\) and \(B=\{4,6,8,10,12,14\}\), what is \(B\setminus A\)?
Answer and explanation
Correct answer: \(\varnothing\)
The composite natural numbers not exceeding 15 include \(4,6,8,9,10,12,14,15\) (and the convention that 1 is neither prime nor composite is used). Every element of \(B=\{4,6,8,10,12,14\}\) is therefore an element of \(A\), so \(B\subseteq A\). The difference \(B\setminus A\) contains elements in B that are absent from A; there are none. Hence \(B\setminus A=\varnothing\), making option A correct.
Frequently asked questions
What is the correct answer to this question?
\(\varnothing\)
Why is this the correct answer?
The composite natural numbers not exceeding 15 include \(4,6,8,9,10,12,14,15\) (and the convention that 1 is neither prime nor composite is used). Every element of \(B=\{4,6,8,10,12,14\}\) is therefore an element of \(A\), so \(B\subseteq A\). The difference \(B\setminus A\) contains elements in B that are absent from A; there are none. Hence \(B\setminus A=\varnothing\), 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).
