Question

离散数学等价关系和商集，求解答

Answer 1

（1）证明满足自反性、对称性、传递性，即可。

自反性：|U|=|U| ⇔ URU

对称性：
|U|=|V| ⇔ |V|=|U|
则 URV ⇔ VRU

传递性：
|U|=|V| ，|V|=|W| ⇒ |U|=|W|
则 URV ∧ VRW ⇔ URW

（2）
P(A)/R={{∅},
{{1},{2},{3},{4},{5},{6}},
{{1,2},{1,3},{1,4},{1,5},{1,6},{2,3},{2,4},{2,5},{2,6},{3,4},{3,5},{3,6},{4,5},{4,6},{6,6}},
{{1,2,3},{1,3,4},{1,3,5},{1,3,6},{2,3,4},{2,3,5},{2,3,6},{1,2,4},{2,4,5},{2,4,6},{1,4,5},{2,5,6},{1,4,6},{1,2,5},{3,4,5},{3,4,6},{1,5,6},{3,5,6},{1,2,6},{3,4,5}},
{{2,3,4,6},{1,2,4,5},{1,2,4,6},{1,2,3,6},{2,3,4,5},{1,4,5,6},{1,2,3,5},{3,4,5,6},{1,2,3,4},{2,3,5,6},{1,3,4,5},{1,3,4,6},{1,2,5,6},{2,4,5,6},{1,3,5,6}},
{{1,2,3,5,6},{2,3,4,5,6},{1,2,3,4,5},{1,3,4,5,6},{1,2,4,5,6},{1,2,3,4,6}},
{{1,2,3,4,5,6}}
}