If \(A=\{1,2,3\}\) and \(B=\{2,3,4\}\), which statement is correct?
Answer and explanation
Correct answer: Neither \(A\subseteq B\) nor \(B\subseteq A\)
For \(A\subseteq B\), every element of A must belong to B. This fails because 1 belongs to A but not to B. Similarly, \(B\subseteq A\) is false because 4 belongs to B but not to A. The sets are also not equal, although they share the elements 2 and 3. Therefore neither set is a subset of the other, so option D is correct. Common elements alone do not establish a subset relation.
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?
For \(A\subseteq B\), every element of A must belong to B. This fails because 1 belongs to A but not to B. Similarly, \(B\subseteq A\) is false because 4 belongs to B but not to A. The sets are also not equal, although they share the elements 2 and 3. Therefore neither set is a subset of the other, so option D is correct. Common elements alone do not establish a subset relation.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
