Re: [理工] [離散]-證明等價關係
※ 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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◆ From: 114.39.16.163
推
03/31 05:18, , 1F
03/31 05:18, 1F
推
03/31 05:21, , 2F
03/31 05:21, 2F
→
03/31 06:44, , 3F
03/31 06:44, 3F
推
03/31 08:27, , 4F
03/31 08:27, 4F
→
03/31 08:27, , 5F
03/31 08:27, 5F
推
03/31 08:33, , 6F
03/31 08:33, 6F
推
03/31 19:21, , 7F
03/31 19:21, 7F
推
03/31 19:39, , 8F
03/31 19:39, 8F
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