Let N be the set of natural numbers and a relation R on N be defined by R = {(x,y) ∈ N×N : x³ - 3x²y – xy² + 3y³ = 0} . Then the relation R is :
Let N be the set of natural numbers and a relation R on N be defined by R = {(x,y) ∈ N×N : x³ - 3x²y – xy² + 3y³ = 0} . Then the relation R is :
Option 1 -
Reflexive but neither symmetric nor transitive
Option 2 -
An equivalence relation
Option 3 -
Symmetric but neither reflexive nor transitive
Option 4 -
Reflexive and symmetric, but not transitive
Asked by Shiksha User
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1 Answer
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Correct Option - 3
Detailed Solution:for reflexive (x, x)
x³ - 3x²x + 3x³ = 0
. reflexive
For symmetric
(x, y)? R
x³ - 3x²y - xy² + 3y³ = 0
? (x - 3y) (x² - y²) = 0
For (y, x)
(y - 3x) (y² - x²) = 0
? (3x - y) (x² - y²) = 0
Not symmetric
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