If \(A=\{a,b,c\}\) and \(B=\{b,c,d\}\), which of the following statements is correct?
Answer and explanation
Correct answer: Neither \(A\subseteq B\) nor \(B\subseteq A\)
Two sets are equal only when they contain exactly the same elements. Here, \(a\in A\) but \(a\notin B\), while \(d\in B\) but \(d\notin A\), so \(A\ne B\). Since one missing element is enough to disprove a subset relation, \(A\not\subseteq B\); similarly, \(B\not\subseteq A\). Therefore, neither set is a subset of the other. The correct answer is D.
Frequently asked questions
What is the correct answer to this question?
Neither \(A\subseteq B\) nor \(B\subseteq A\)
Why is this the correct answer?
Two sets are equal only when they contain exactly the same elements. Here, \(a\in A\) but \(a\notin B\), while \(d\in B\) but \(d\notin A\), so \(A\ne B\). Since one missing element is enough to disprove a subset relation, \(A\not\subseteq B\); similarly, \(B\not\subseteq A\). Therefore, neither set is a subset of the other. The correct answer is D.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
