For each of the following relations, state whether or not it is reflexive whether or not it is sy...1 answer below »

For each of the following relations, state whether or not it is reflexive whether or not it is symmetric, whether or not it is transitive, whether or not it is antisymmetric, and whether or not it is a partial order. For each example, let the set S on which the relation is defined be the set of elements mentioned in that example. (a) {(a, a)} (b) {(a, b), (a, c), (b, c)} (c) {(a, a), (a, b), (b, b), (b, c), (a, c), (c, c)} (d) {(a, b), (b, c)} (e) {}

1 Approved Answer

katraju m
answered on
August 30, 2020

5
Ratings,(12 Votes)

a) The given relation is reflexive as (a,a) the relation is neither symmetric, nor antisymmetric as only (a,a). it
is not transitive as well and hence not a partial order
b) The relation set is (a,b),(a, c),(b,c)
As (a, a),(6,6), (c,c) ¢(a,b),(a, e), (b,c) so the relation is not reflexive
Also (a, b) € (a,b),(a, c), (b,c) but (b, a) a,b),(a,...

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