For A={0,1,2,3,4,5} and R={(a,b): a²≡b² (mod 6)}, how many equivalence classes does R have?
Answer and explanation
Correct answer: 4
Option C is correct. The squares modulo 6 are: 0²≡0, 1²≡1, 2²≡4, 3²≡3, 4²≡4, and 5²≡1. Thus the elements group according to equal square residues into the classes {0}, {1,5}, {2,4}, and {3}. There are therefore four equivalence classes. The relation is based on equality of residues, so elements in the same listed group relate to one another, while elements in different groups do not.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
Option C is correct. The squares modulo 6 are: 0²≡0, 1²≡1, 2²≡4, 3²≡3, 4²≡4, and 5²≡1. Thus the elements group according to equal square residues into the classes {0}, {1,5}, {2,4}, and {3}. There are therefore four equivalence classes. The relation is based on equality of residues, so elements in the same listed group relate to one another, while elements in different groups do not.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Reflexive relation.
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