The relation S = { (3,3) (4,4) } on the set A = {3,4,5} is
A. Not reflexive but symmetric and transitive
B. Reflexive only
C. Symmetric only
D. An equivalence relation
Hint: Let’s consider elements of a set as a,b and c and go with the definition of reflexive, symmetric and transitive.
Complete step by step answer:
As given that set is A = 3,4,5} and the relation is S = { (3,3) (4,4) }
And as we know the relation above will not be reflexive because every element of A is not related to itself as (5,5) is absent.
But A is symmetric because if for all a and b in A that a is related to b if and only if b is related to a.
And also A is transitive because if a is related to b and b is related to c then a is also related to c.
Hence we can conclude that the given relation is not reflexive but symmetric and transitive.
So, the correct option is A.
Note: Whenever you come up with this type of problem where it is asked about relation with set, a better knowledge of definitions will be an added advantage.
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