Discussion
The relation R={(1,3),(2,3),(2,4),(3,1)(4,4)(4,1)} on the set X={1,2,3,4} is
Answer: D
The relation is not symmetric.
A relation is symmetric when every pair (a, b) comes with its reverse (b, a). R contains (2, 3) but not (3, 2), and (2, 4) but not (4, 2), so it fails the test.
The other properties fail too. R is not reflexive, since (1, 1), (2, 2) and (3, 3) are missing. It is not transitive: (2, 3) and (3, 1) are in R but (2, 1) is not. It is not a function at all, because 2 is paired with both 3 and 4, so it can be neither one-one nor onto.
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