If \(A=\{1,2,3,4\}\) and \(B=\{1,2\}\), which statement is correct?
Answer and explanation
Correct answer: \(B\subset A\) and \(B\ne A\)
Every element of B, namely 1 and 2, is also an element of A. Therefore \(B\subseteq A\). However, A also contains 3 and 4, which are not in B, so the two sets are not equal. Consequently B is a proper subset of A, written \(B\subset A\) when the symbol denotes a proper subset. Option A reverses the inclusion, option C claims equality, and option D is false because the intersection is \(\{1,2\}\), not empty.
Frequently asked questions
What is the correct answer to this question?
\(B\subset A\) and \(B\ne A\)
Why is this the correct answer?
Every element of B, namely 1 and 2, is also an element of A. Therefore \(B\subseteq A\). However, A also contains 3 and 4, which are not in B, so the two sets are not equal. Consequently B is a proper subset of A, written \(B\subset A\) when the symbol denotes a proper subset. Option A reverses the inclusion, option C claims equality, and option D is false because the intersection is \(\{1,2\}\), not empty.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
