A relation R on the set of all integers is defined by xRy if 2x + 3y is divisible by 5. Which property does R satisfy? A. reflexive only B. symmetric only C. transitive only D. reflexive, symmetric and transitive Answer: D) reflexive, symmetric and transitive Explanation: Reflexive: 2x + 3x = 5x, divisible by 5. Symmetric: If 2x + 3y = 5k, then 2y + 3x = 5(x+y) − (2x+3y) = 5(x+y−k) divisible by 5. Transitive: If 2x+3y = 5k and 2y+3z = 5m, then 2x+3z = (2x+3y)+(2y+3z)−5y = 5(k+m−y). Thus equivalence.

imo class 12 relations and functions

A relation R on the set of all integers is defined by xRy if 2x + 3y is divisible by 5. Which property does R satisfy?

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A relation R on the set of all integers is defined by xRy if 2x + 3y is divisible by 5. Which property does R satisfy?

A. reflexive only
B. symmetric only
C. transitive only
D. reflexive, symmetric and transitive

Answer: D) reflexive, symmetric and transitive

Explanation: Reflexive: 2x + 3x = 5x, divisible by 5. Symmetric: If 2x + 3y = 5k, then 2y + 3x = 5(x+y) − (2x+3y) = 5(x+y−k) divisible by 5. Transitive: If 2x+3y = 5k and 2y+3z = 5m, then 2x+3z = (2x+3y)+(2y+3z)−5y = 5(k+m−y). Thus equivalence.

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