The relation R in the set \(\{1, 2, 3\}\) given by \(R = \{(1, 1), (2, 2), (3, 3), (1, 2), (1, 3), (2, 3)\}\) is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → both reflexive and transitive
Reflexive: (1, 1), (2, 2) and (3, 3) are all in R, so R is reflexive.
Symmetric: (1, 2) is in R but (2, 1) is not, so R is not symmetric.
Transitive: pairs of the form (a, a) never create a new requirement. The only chain of two pairs with different elements is
\((1, 2), (2, 3) \in R\)
and it needs (1, 3), which is in R. So R is transitive.
Hence R is reflexive and transitive, but not symmetric.