On the real numbers, define aRb if and only if |a|=|b|. What is the equivalence class of -3?
Answer and explanation
Correct answer: {-3,3}
The class [-3] consists of every real number x satisfying |x|=|-3|=3. The only real numbers with absolute value 3 are -3 and 3, so [-3]={-3,3}. This relation is an equivalence relation because equality of absolute values is reflexive, symmetric, and transitive; however, the class is not the whole real line.
Frequently asked questions
What is the correct answer to this question?
{-3,3}
Why is this the correct answer?
The class [-3] consists of every real number x satisfying |x|=|-3|=3. The only real numbers with absolute value 3 are -3 and 3, so [-3]={-3,3}. This relation is an equivalence relation because equality of absolute values is reflexive, symmetric, and transitive; however, the class is not the whole real line.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Types of relations.
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