By using the concept of relation, it can be proved that
If R is a Reflexive relation, then is a Reflexive relation
If R is a Symmetric relation, then is a Symmetric relation
If R is a Transitive relation, then is a Transitive relation
What is a relation?
Relation on a set is the subset of the cartesian product
A)
Let R be a reflexive relation .
Let (x, x) ∈ R
Then (x, x) ∈
So is reflexive
B)
Let R be a symmetric relation such that holds
so yRx holds
Since R is symmetric, xRy holds
hold
is symmetric
C)
Let R be a transitive relation such that and holds
Then yRx and zRy holds
Since R is transitive
zRx holds
holds
is transitive
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Complete Question
Let R Be A Relation On A Set A. Prove The Following: A) If R Is Reflexive, Then Is Reflexive. B) If R Is Symmetric, Then Is Symmetric. C) If R Is Transitive, Then Is Transitive.