.R {(a,b), (b,c),(a,c)} is it symmetric? When A={a,b,c}
Answers
Answer:
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Answer:
R={(1,1)} on set A is not irreflexive. Symmetric: A relation is symmetric if for all a ,b belonging to set A if (a ,b) belongs to relation then (b ,a) also belongs to relation where a ,b belongs to set A. Since relation R contains 0 but set does not contain element 0. Hence, this relation is incorrect.
Step-by-step explanation:
IT IS REFLEXIVE AND TRANSITIVE.
REFLEXIVE-
A relation R on a set A is called reflexive if (a, a) ∈ R for every element a ∈ A.
SINCE (a, a), (b, b), (c, c) are present, it is reflexive.
TRANSITIVE -
A relation R on a set A is called transitive if whenever (a, b) ∈ R and (b, c) ∈ R, then
(a, c) ∈ R, for all a, b, c ∈ A.
SINCE (a, b), (b, c) and (c, a) are present.
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