Let \(A = \{1, 2, 3, 4, 5, 6\}\) and let R be the relation on A given by \(R = \{(a, b) : b = a + 2\}\). Then R is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → neither reflexive, nor symmetric, nor transitive
Listing the pairs with \(b = a + 2\) and both entries in A:
\(R = \{(1, 3), (2, 4), (3, 5), (4, 6)\}\)
Not reflexive: (1, 1) is not in R, since \(1 \ne 1 + 2\).
Not symmetric: (1, 3) is in R, but (3, 1) is not, since \(1 \ne 3 + 2\).
Not transitive: (1, 3) and (3, 5) are in R, but (1, 5) is not, since \(5 \ne 1 + 2\).
So R has none of the three properties.