Question

The relation S = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5)} on {1, 2, 3, 4, 5} is.......,Select Proper option from the given options.
(a) symmetric only
(b) reflexive only
(c) transitive only
(d) an equivalence relation

Answer 1

Answer:

(b) reflexive only.

Step-by-step explanation:

Given S={(1,1)(2,2)(3,3)(4,4)(5,5)} on {1,2,3,4,5}.

If (a,a)∈S  then it should be reflexive relation.

If (a,b)∈S ⇒ (b,a) ∈S then it is symmetric relation.

If (a,b)∈S, (b,c)∈S ⇒(a,c) then it is transitive relation.

If in a relation all the relations like reflexive, symmetric and transitive are present then it will be equivalence relation. [a,b, c are the elements of the relation and S is the relation.

It is the  only reflexive relation because in this (1,1)(2,2)(3,3)(4,4)(5,5)∈S.But   (a,b)∈S ⇒ (b,a) ∈S  and  (a,b)∈S, (b,c)∈S ⇒(a,c)  does not satisfied. Hence it is only reflexive relation.

Answer 2

Answer:

(B)

Step-by-step explanation:

it is reflexive only