Question #20079

For each of the following relations, indicate whether they are reflexive, symmetric, and transitive (for example select reflexive and transitive if the relation is reflexive and transitive, but not symmetric).
(a) Let R be the relation on N given by xRy if and only if x divides y.
(b) Let X be a set and let R be the relation "⊆" on . In other words, SRT if and only if S⊆T.
(c) Let S be the set of people in the world. Define R on S by xRy if and only if x likes y (use common sense)
(d) Let R be the relation {(1,1), (1,2), (2,2),(1,3),(3,3)} on the set {1,2,3}.
(e) Let R be the relation on R given by xRy if and only if x−y∈Q.
(f) Let R be the relation on R given by xRy if and only if x−y∉Q.
(g) Let R be the relation on R given by xRy if and only if (x−y)2<0.
(h) Let R be the the relation on R given by xRy if and only if |x-y|≤2
(i) Let R be the relation {(1,1), (1,2), (1,3), (2,1), (2,2),(3,1)} on the set {1,2,3}.
(j) Let R be the relation on R given by xRy if and only if xy∈Q.

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