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.
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}
(i) A = {1,2,3,.....,13,14}
R = {x.y) : 3 x – y ≠} = {(x, y) : y = 3 x}
= {(1,3), (2, 6), (3, 9), (4, 12)}
(a) R is not reflexive as (x, x) ∉ R [ ∵ 3 x – x ≠ 0]
(b) R is not symmetric as (x,y) ∈ R does not imply (y, x) ∈ R
[ ∴ (1, 3) ∈ R does not imply (3. 1) ∈ R]
(c) R is not transitive as (1.3) ∈ R , (3, 9) ∈ R but (1.9) ∉ R.
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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