If A = {{1, 2}, {2, 1}}, what is n(A)?
Answer and explanation
Correct answer: 1
In a set, the order of elements does not matter. Hence {1, 2} and {2, 1} represent exactly the same inner set. The outer set A therefore contains only one distinct element, namely the set {1, 2}. Consequently, the cardinality of A is n(A) = 1, not 2. Repeated or differently ordered descriptions do not create new elements in a set.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
In a set, the order of elements does not matter. Hence {1, 2} and {2, 1} represent exactly the same inner set. The outer set A therefore contains only one distinct element, namely the set {1, 2}. Consequently, the cardinality of A is n(A) = 1, not 2. Repeated or differently ordered descriptions do not create new elements in a set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
