2) S is a relation over the set R of all real numbers and it given by
(a,b) € S<=>ab 0.
Them, S is
a) symmetric and transitive only
b) reflexive and symmetric only
c) a partial order relation
d) an equivalence relation
Answers
Answered by
2
S is an equivalence relation.
Option (d) is correct.
Step-by-step explanation:
Symmetric relation:
(a,b)∈ S ⇔ ab ≥ 0
Similarly,
(b,a)∈ S ⇔ ba ≥ 0
ab ≥ 0 when a > 0, b > 0 or a < 0, b < 0
Reflexive relation:
(a,a)∈ S ⇔ a^2 ≥ 0
Transitive relation:
(a,b)∈ S ⇔ ab ≥ 0
(b,c)∈ S ⇔ bc ≥ 0
ab^2c ≥ 0
No multiplying the above values we get.
ac ≥ 0
(a,c)∈ S ⇔ ac ≥ 0
Thus, S is an equivalence relation.
Answered by
0
Answer :-
S is an equivalence relation.
Option (d) is correct.
Step-by-step explanation:
Symmetric relation:
(a,b)∈ S ⇔ ab ≥ 0
Similarly,
(b,a)∈ S ⇔ ba ≥ 0
ab ≥ 0 when a > 0, b > 0 or a < 0, b < 0
Reflexive relation:
(a,a)∈ S ⇔ a^2 ≥ 0
Transitive relation:
(a,b)∈ S ⇔ ab ≥ 0
(b,c)∈ S ⇔ bc ≥ 0
ab^2c ≥ 0
No multiplying the above values we get.
ac ≥ 0
(a,c)∈ S ⇔ ac ≥ 0
Thus, S is an equivalence relation.
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