Let S be the smallest possible relation on the set {a, b, c, d} that is reflexive, symmetric, but not transitive. Then, the number of elements in S isQuestion 1Answera.None of the Given Choicesb.8c.10d.2e.6f.4

A relation is reflexive if every element is related to itself. So, for the set {a, b, c, d}, we need at least 4 elements in S for the relation to be reflexive: (a,a), (b,b), (c,c), (d,d).

A relation is symmetric if for every element that is related to another, that other element is also related to the first. This doesn't require us to add any more elements to S, because the reflexive pairs already satisfy this condition.

However, we want the relation to not be transitive. A relation is transitive if whenever an element is related to a second, and that second is related to a third, then the first is also related to the third. To ensure our relation is not transitive, we can add one more pair to S: (a,b). Now, we have a relation that is reflexive and symmetric, but not transitive, because a is related to b (from the pair we added), and a is related to a (from the reflexive pairs), but b is not related to a.

So, the smallest possible S that satisfies these conditions has 5 elements: (a,a), (b,b), (c,c), (d,d), (a,b). Therefore, none of the given choices are correct.