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  • Prove that the following relation defined on the set of inetegers z :  R= {(x,y):2x-2y is an integer} Are 1. Reflexive     2. Symmetric   3.

Prove that the following relation defined on the set of inetegers z : 

R= {(x,y):2x-2y is an integer}

Are 1. Reflexive 

   2. Symmetric

  3. Transitive

 

Answers (1)

best_answer

Reflexive:

\(x \in Z\), \(2 x-2 x=0\) (integer).

Symmetric:

\text { If }(x, y) \in R \text {, then } 2 x-2 y is integer

\text { Thus, } 2 y-2 x=-(2 x-2 y) \text { is also integer. }

Transitive:

\text { If }(x, y) \in R \text { and }(y, z) \in R \text {. }

\text { then } 2 x-2 y \text { and } 2 y-2 z \text { are integers. }

\text { Adding: }(2 x-2 y)+(2 y-2 z)=2 x-2 z \text { (integer). }

Posted by

Divya Sharma

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