If \(A=\{1,1,2,2,3\}\) and \(B=\{3,2,1\}\), which statement is true?
Answer and explanation
Correct answer: \(A=B\)
In set notation, repeating an element does not create a new element and multiplicity is ignored. Therefore \(A=\{1,2,3\}\) after removing repeated entries. The elements of \(B\) are also \(\{1,2,3\}\), merely written in a different order. Since two sets are equal when they contain exactly the same elements, \(A=B\). Neither proper-subset option is correct because neither set has an additional element, and option D contradicts their equality.
Frequently asked questions
What is the correct answer to this question?
\(A=B\)
Why is this the correct answer?
In set notation, repeating an element does not create a new element and multiplicity is ignored. Therefore \(A=\{1,2,3\}\) after removing repeated entries. The elements of \(B\) are also \(\{1,2,3\}\), merely written in a different order. Since two sets are equal when they contain exactly the same elements, \(A=B\). Neither proper-subset option is correct because neither set has an additional element, and option D contradicts their equality.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
