Let R be the relation on Z ( the set of integers ) defined by ( x , y ) i n R iff x 2 y 2 2 k for some integers k 0 R is symmetric Which one of the following is a valid proof showing that R is symmetric a Let x , yinZ be given Suppose ( x , y ) i n R then x 2 y 2 2 k for some k 0 ie y 2 x 2 2 k for some k 0 thus ( x , y ) i n R b Let x , yinZ be given Suppose ( x , y ) i n R then x 2 y 2 2 k for some k 0 ie y 2 x 2 2 k for some k 0 thus ( y , x ) i n R c Let x , yinZ be given Suppose ( x , y ) i n R then x 2 y 2 2 k for some k 0 thus ( y , x ) i n R d Let x , yinZ be given Suppose ( x , x ) i n R then x 2 y 2 2 k for some k 0 ie y 2 x 2 2 k for some k 0 thus ( y , y ) i n R

Question

Let R be the relation on Z ( the set of integers ) defined by ( x , y ) i n R iff x 2   y 2   2 k for some integers k 0   R is symmetric  Which one of the following is a valid proof showing that R is symmetric  a   Let x , yinZ be given  Suppose ( x , y ) i n R then x 2   y 2   2 k for some k 0   ie y 2   x 2   2 k for some k 0   thus ( x , y ) i n R   b   Let x , yinZ be given  Suppose ( x , y ) i n R then x 2   y 2   2 k for some k 0   ie y 2   x 2   2 k for some k 0   thus ( y , x ) i n R   c   Let x , yinZ be given  Suppose ( x , y ) i n R then x 2   y 2   2 k for some k 0   thus ( y , x ) i n R   d   Let x , yinZ be given  Suppose ( x , x ) i n R then x 2   y 2   2 k for some k 0   ie y 2   x 2   2 k for some k 0   thus ( y , y ) i n R

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Question: Let R be the relation on Z ( the set of integers ) defined by ( x , y ) i n R iff x

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