On A = {1,2,3,4}, let R = {(a,b) : a + b ≤ 5}. Is R symmetric?
Answer and explanation
Correct answer: Yes, it is symmetric
To test symmetry, assume (a,b) ∈ R. By definition, a+b≤5. Since addition is commutative, b+a has exactly the same value as a+b, so b+a≤5 as well. Therefore (b,a) ∈ R whenever (a,b) ∈ R, which proves that R is symmetric. The relation is not empty—for example, (1,1) belongs to it—and the question does not require testing reflexivity.
Frequently asked questions
What is the correct answer to this question?
Yes, it is symmetric
Why is this the correct answer?
To test symmetry, assume (a,b) ∈ R. By definition, a+b≤5. Since addition is commutative, b+a has exactly the same value as a+b, so b+a≤5 as well. Therefore (b,a) ∈ R whenever (a,b) ∈ R, which proves that R is symmetric. The relation is not empty—for example, (1,1) belongs to it—and the question does not require testing reflexivity.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Symmetric relation.
