Short Answer TypeShow that the relation R in the set A of all the books in a library of a college given by R = {(x, y): x and y have same number of pages} is an equivalence relation.
R = {(a, b) : a ≤ b2}
(i) Since (a, a) ∉ R
∴ R is not reflexive.
(ii) Also (a, b) ∈ R ⇏ (b, a) ∈ R
[Take a = 2 ,b = 6, then 2 ≤ 62 but (6)2 < 2 is not true]
∴ R is not symmetric.
(iii) Now (a, b), (b, c) ∈ R ∉ (a, c) ∈ R
[Take a = 1, b = – 2, c = – 3 ∴ a ≤ b2 . b ≤ c2 but a ≤ c2 is not true) ∴ R is not transitive.
Determine whether each of the following relations are reflexive, symmetric and transitive :
(i) Relation R in the set A = {1, 2, 3,....., 13, 14} defined as R = {(x, y) : 3 x – y = 0}
Determine whether each of the following relations are reflexive, symmetric and transitive :
(ii) Relation R in the set N of natural numbers defined as R = {(x, y) : y = x + 5 and x < 4}
Determine whether each of the following relations are reflexive, symmetric and transitive :
(ii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as R = {(x,y) : y is divisible by x}
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