If \(A=\{1,2,3,4\}\) and \(B=\{2,4,6,8\}\), which statement about \(A\setminus B\subseteq A\) is correct?
Answer and explanation
Correct answer: It is always true
By definition, \(A\setminus B\) is formed by selecting some elements of A and removing those that also occur in B. Every element that remains therefore already belongs to A. Consequently, \(A\setminus B\subseteq A\) is always true for any sets A and B, including when the difference is empty. For these particular sets, \(A\setminus B=\{1,3\}\), which visibly confirms the statement.
Frequently asked questions
What is the correct answer to this question?
It is always true
Why is this the correct answer?
By definition, \(A\setminus B\) is formed by selecting some elements of A and removing those that also occur in B. Every element that remains therefore already belongs to A. Consequently, \(A\setminus B\subseteq A\) is always true for any sets A and B, including when the difference is empty. For these particular sets, \(A\setminus B=\{1,3\}\), which visibly confirms the statement.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
