For the relation on A={1,2,3,4,5,6} defined by “a and b are both multiples of 3 or both are not multiples of 3”, which statement is true?
Answer and explanation
Correct answer: The relation is not antisymmetric
The relation groups the set into the two classes {3,6} and {1,2,4,5}, so it is an equivalence relation and is symmetric. It is not antisymmetric, because for example 1R2 and 2R1 both hold although 1≠2. It therefore has two equivalence classes, not six. Thus option C correctly identifies the additional property that fails.
Frequently asked questions
What is the correct answer to this question?
The relation is not antisymmetric
Why is this the correct answer?
The relation groups the set into the two classes {3,6} and {1,2,4,5}, so it is an equivalence relation and is symmetric. It is not antisymmetric, because for example 1R2 and 2R1 both hold although 1≠2. It therefore has two equivalence classes, not six. Thus option C correctly identifies the additional property that fails.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Types of relations.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
