Question

Consider the relation R = (a,b),(a,c),(c,c),(b,b),(c,b),(b,c) on the set A = a,b. Is R reflexive? Symmetric? Transitive? and why or why not.

Answer 1

First off, you'd better have A={a,b,c} or the relation R is not over set A.

reflexive: (a,a)? No
Symmetric: (a,b) and (b,a)? No
Transitive: Yes, since
(a,b),(b,c) and (a,c)
(a,b),(b,b)
(a,c),(c,b) and (a,b)
(b,c),(c,b) and (b,b)
(b,c),(c,c)
(c,b),(b,c) and (c,c)

Answer 2

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