中央111 離散數學與線性代數第7題｜離散數學 Ch10 偏序集、格、布林代數與命題邏輯

離散數學›Ch10 偏序集、格、布林代數與命題邏輯

第 18 題／共 18 題

18. Partial Order、Total Order、Lattice、Well Order

#LS-10-018中Partial OrderTotal OrderLatticeWell Order

Consider a predicate $P(i, j)$ , where $i, j$ are elements from the same domain $S$ . Suppose all following statements are true:

\forall i, p(i, i);\quad \forall i, j, (i \ne j), p(i, j) \rightarrow \neg p(j, i);\quad \forall i, j, k, \big(p(i, j) \wedge p(j, k)\big) \rightarrow p(i, k);

\forall i, j, p(i, j) \vee p(j, i);\quad \exists! k, \forall i \ne k, p(k, i);

( $\exists!$ means "exist one and only one")

Which of the following options are correct?

📄 中央111

▤完整推導請見《WH 資工筆記 · 離散數學》Ch10 偏序集、格、布林代數與命題邏輯

本章題號 · 1–18 / 18