On A = {1, 2, 3}, let R = {(a, b) : a + b = 4}. Why is R not reflexive?
Answer and explanation
Correct answer: Because a + a = 4 is not true for every a
A relation R on A is reflexive only when (a, a) belongs to R for every a in A. Here, the required condition becomes a + a = 4, or 2a = 4. It is true for a = 2, so (2, 2) is present, but it is false for a = 1 and a = 3; therefore (1, 1) and (3, 3) are absent. Since even one required self-pair is missing, R is not reflexive. Thus option A is correct; options B and C merely identify true individual facts, while D is irrelevant.
Frequently asked questions
What is the correct answer to this question?
Because a + a = 4 is not true for every a
Why is this the correct answer?
A relation R on A is reflexive only when (a, a) belongs to R for every a in A. Here, the required condition becomes a + a = 4, or 2a = 4. It is true for a = 2, so (2, 2) is present, but it is false for a = 1 and a = 3; therefore (1, 1) and (3, 3) are absent. Since even one required self-pair is missing, R is not reflexive. Thus option A is correct; options B and C merely identify true individual facts, while D is irrelevant.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Reflexive relation.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
