If \(\{a+2\}=\{9\}\), what is the value of \(a\)?
Answer and explanation
Correct answer: 7
Each side is a singleton set, meaning that each set has exactly one element. Two singleton sets are equal only when their sole elements are equal, so \(a+2=9\). Subtracting 2 from both sides gives \(a=7\), which is option C. The braces indicate sets; they do not change the equality principle. A common error is to add 2 to 9 and choose 11, but the equation requires subtraction because 2 is already added to \(a\).
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
Each side is a singleton set, meaning that each set has exactly one element. Two singleton sets are equal only when their sole elements are equal, so \(a+2=9\). Subtracting 2 from both sides gives \(a=7\), which is option C. The braces indicate sets; they do not change the equality principle. A common error is to add 2 to 9 and choose 11, but the equation requires subtraction because 2 is already added to \(a\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
