Relation R on the set \(A= \{1,2, ....... 15\}\) defined as \(R = \{(x, y): y- 4x = 0\}\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Neither Reflexive nor symmetric
Here y = 4x, and y must also lie in A, so \(4x \le 15\), that is \(x \le 3\):
\(R = \{(1, 4), (2, 8), (3, 12)\}\)
Reflexive needs (a, a) in R for every a in A. But \((1, 1) \notin R\) (it would need 1 = 4). So R is not reflexive.
Symmetric needs (b, a) in R whenever (a, b) is in R. But \((1, 4) \in R\) while \((4, 1) \notin R\). So R is not symmetric.
Hence R is neither reflexive nor symmetric.