On A = {1,2,3,4}, let R = {(a,b) : a + b = 5}. What type of relation is R?
Answer and explanation
Correct answer: Symmetric but not reflexive
The condition defining R is a+b=5. If (a,b) satisfies it, then reversing the components gives b+a=5 because addition is commutative; hence (b,a) also belongs to R, so R is symmetric. Reflexivity would require (a,a) for every a in A. But for a=1, 1+1≠5, and similarly the diagonal pairs are absent. Therefore R is symmetric but not reflexive.
Frequently asked questions
What is the correct answer to this question?
Symmetric but not reflexive
Why is this the correct answer?
The condition defining R is a+b=5. If (a,b) satisfies it, then reversing the components gives b+a=5 because addition is commutative; hence (b,a) also belongs to R, so R is symmetric. Reflexivity would require (a,a) for every a in A. But for a=1, 1+1≠5, and similarly the diagonal pairs are absent. Therefore R is symmetric but not reflexive.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Symmetric relation.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesWrite a review / Rate this question
Student Reviews
No published reviews yet.
