Let \(A = \{2, 3, 4, 6, 8, 12\}\) and let R be the relation on A given by \(R = \{(a, b) : a \text{ divides } b\}\). Then R is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → reflexive and transitive but not symmetric
Reflexive: every number divides itself, so (a, a) is in R for every a in A.
Not symmetric: 2 divides 4, so (2, 4) is in R. But 4 does not divide 2, so (4, 2) is not in R.
Transitive: if a divides b and b divides c, write
\(b = ka\) and \(c = mb\)
\(c = (mk)a\)
so a divides c.
Hence R is reflexive and transitive but not symmetric.