【問題】離散的等價問題 拜託 我一直卡住

[gn00618777 10]

題目是這樣

Let X={1,2,3,4,5}, Y={3,4}, and C={1,3}.Define the relation R on

P(X)，the set of all subsets of X，as ARB if A∪Y＝B∪Y

(a)Show that R is equvilence (這題我証出來了)

(b)List the elements of [C]，the equvilence class containing C.

©How many distinct equivalence classes are there?

(b)和©我有疑問。 以下是解答

(b) ∵ CUY= {1,3}U{3,4}={1,3,4} →[C]={{1},{1,3},{1,4},{1,3,4}

為什麼沒有{3,4} 他也是[C]的等價類阿....？

如果可以能說說這題的意思嗎？

©【{}】= {{},{3},{4},{3,4}}

【{1}】= {{1},{1,3},{1,4},{1,3,4}}

【{2}】= {{2},{2,3},{2,4},{2,3,4}}

【{5}】= {{5},{3,5},{4,5},{3,4,5}}

【{1,2}】 = {{1,2},{1,2,4},{1,2,3},{1,2,3,4}}

【{1,5}】 = {{1,5},{1,3,5},{1,4,5},{1,3,4,5}}

【{2,5}】 = {{2,5},{2,3,5},{2,4,5},{2,3,4,5}}

【{1,2,5}】 = {{1,2,5},{1,2,3,5},{1,2,4,5},{1,2,3,4,5}}

→ There are 8 equivalence classes in the partition induced by R

這題我更不懂了= = 怎麼沒[{3}] 或者 [{4}]阿.. 我一定等價類沒學好....

[gn00618777 10]

沒事了=.= 睡一覺來忽然就懂了

[筱釵 10]

所以 請問原PO

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