Discussion
The relation \(R = \{(4, 4)(4, 5), (5, 7), (4, 8), (5, 5), (7, 8),\) \((7, 7), (7, 5), (8, 8), (8, 7), (8, 5), (9, 9)\}\) on the set \(A = \{4, 5, 7, 8, 9\}\) is
Answer: C
The relation is reflexive.
Every element of A is related to itself: (4, 4), (5, 5), (7, 7), (8, 8) and (9, 9) are all in R.
It is not symmetric, because (4, 5) is in R but (5, 4) is not. It is not transitive, because (4, 5) and (5, 7) are in R but (4, 7) is not. Without symmetry and transitivity it is not an equivalence relation, and it is not a function because 4 is paired with 4, 5 and 8.
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