Consider the relation R on the set {-2,-1,0,1,2} defined by (a,b) ∈ R if and only if 1+ab>0.
Then among the statements:
I. The number of elements in R is 17
II. R is an equivalence relation
Reflexive If (a, a) ∈ R ⇒ 1 + a2 > 0 ⇒ It is reflexive relation
Symmetric If 1 + ab > 0 ⇒ 1 + ba > 0 i.e. If (a, b) ∈ R and (b, a) ∈ R Therefore it is symmetric relation
Transitive ∵ (–2, 0) ∈ R & (0, 2) ∈ R But (–2, 2) ∉ R Hence it is not transitive ⇒ It is not an equivalence relation.
Check Number of elements in R ∵ 1 + ab > 0 a & b each can be filled by 5 ways
∴ total elements = 25 But out of these (–2, –1), (–2, 2), (–1, 2), (1, –2), (2, –2), (2, –1) (–1, 1) & (1, –1) are not in relation
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