Let R be the relation on the set Z of all integers defined by \(R = \{(a, b) : a + b \text{ is odd}\}\). Then R is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → symmetric but neither reflexive nor transitive
Reflexive fails: for every integer a,
\(a + a = 2a\), which is even
so no pair (a, a) is in R.
Symmetric holds: \(b + a = a + b\), so if \(a + b\) is odd, so is \(b + a\).
Transitive fails:
\((1, 2) \in R\), since \(1 + 2 = 3\)
\((2, 3) \in R\), since \(2 + 3 = 5\)
\((1, 3) \notin R\), since \(1 + 3 = 4\)
So R is symmetric but neither reflexive nor transitive.