Re: [理工] [離散]-證明等價關係

[sodas2002 (sodas)]

※ 引述《fj90406 (阿亮)》之銘言：
: Let A = Z+ * Z+ a relation R on A as follows:
:     (x,y)R(u,v) if and only if x*v=y*u.
: (1) Prove that R is an equivalent relation.
      For All x,y ∈Z+, x*y=y*x
          --> (x,y)R(x,y) --> Reflexive

      For All x,y,z,w ∈Z+, if x*w=y*z, then z*y=w*x
          --> ∀(x,y)R(z,w) ∃(z,w)R(x,y) --> Symmetric

      For All x,y,z,w,a,b∈Z+, if ∃(x,y)R(z,w)^(z,w)R(a,b)
          --> x*w=y*z ^ z*b=w*a
          ,,,,, No Transitive

      So, this is not an equivalent relation.

: (2) Computer the equivalence class of (5,4)

      Not exists.

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推 sswy7121:transitive應該成立吧...x*w*z*b=y*z*w*a->(x,y)R(a,b)
推 sswy7121:ER(5,4)={(x,y)|4x-5y=0}
→ sodas2002:哦 sorry 樓上對 昨天想睡覺了@@
推 fj90406:問sswy7121大大 第2題那個通式 會滿足反身性嗎?
→ fj90406:找不到(x,y) 然後x=y的
推 fj90406:順便感謝sodas2002大大 想睡覺還打那多回答我 給個讚@@
推 sswy7121:他的element的定義應該是(x,y)...你可能有點誤解囉...
推 sswy7121:所以(5,4)R(5,4)具有反身性...