On A = {1,2,3,4,5}, for aRb when a ≡ b (mod 3), what is the equivalence class [2]?
Answer and explanation
Correct answer: {2,5}
The equivalence class [2] consists of every element x in A that is congruent to 2 modulo 3; equivalently, x − 2 must be divisible by 3. Check the elements of A: 2 − 2 = 0, which is divisible by 3, and 5 − 2 = 3, which is also divisible by 3. For 1, the difference is −1; for 3, it is 1; and for 4, it is 2, none of which is divisible by 3. Therefore [2] = {2,5}. The set {1,4} is the class of 1, while {3} is the class of 3 within A. Since different congruence classes partition A, the whole set cannot be [2]. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
{2,5}
Why is this the correct answer?
The equivalence class [2] consists of every element x in A that is congruent to 2 modulo 3; equivalently, x − 2 must be divisible by 3. Check the elements of A: 2 − 2 = 0, which is divisible by 3, and 5 − 2 = 3, which is also divisible by 3. For 1, the difference is −1; for 3, it is 1; and for 4, it is 2, none of which is divisible by 3. Therefore [2] = {2,5}. The set {1,4} is the class of 1, while {3} is the class of 3 within A. Since different congruence classes partition A, the whole set cannot be [2]. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Equivalence relation.
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