let A = {a, b, c} and R = {(a,a)(b,b)(c,c)(b,c)} be a relation on A then R a] reflexive and symmetric b] reflexive and anti - symmetric c] transitive d] (a) and (c) e] (b) and (c)
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Answer: Binary Relation
Definition: Let A, B be any sets. A binary relation R from A to B, written R : A × B, is a subset
of the set A × B.
Complementary Relation
Definition: Let R be the binary relation from A to B. Then the complement of R can be defined
by R = {(a, b)|(a, b) 6∈ R} = (A × B) − R
Inverse Relation
Definition: Let R be the binary relation from A to B. Then the inverse of R can be defined by
R−1 = {(b, a)|(a, b) ∈ R}
Relations on a Set
Definition: A relation on a set A is a relation from A to A. In other words, a relation on a set A is
a subset of A × A.
Digraph
Definition: A directed graph, or digraph, consists of a set V of vertices (or nodes) together with
a set E of ordered pairs of elements of V called edges (or arcs). The vertex a is called the initial
vertex of the edge (a, b), and the vertex b is called the terminal vertex of this edge.
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