If \(\{2,a\}=\{5,2\}\), what is the value of \(a\)?
Answer and explanation
Correct answer: 5
Equal sets must contain exactly the same elements, and the order in which elements are written is irrelevant. Both sets already contain the element \(2\). For the sets to be equal, the remaining element in the first set must be the remaining element in the second set, namely \(5\). Therefore \(a=5\). If \(a=2\), the first set would reduce to \(\{2\}\), which would not equal \(\{2,5\}\); the other numerical choices introduce an element not present in the second set.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
Equal sets must contain exactly the same elements, and the order in which elements are written is irrelevant. Both sets already contain the element \(2\). For the sets to be equal, the remaining element in the first set must be the remaining element in the second set, namely \(5\). Therefore \(a=5\). If \(a=2\), the first set would reduce to \(\{2\}\), which would not equal \(\{2,5\}\); the other numerical choices introduce an element not present in the second set.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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