[離散] 作業懶人包
鑒於接下來作業有一堆在課本裡面，特將習題PO出以造福同學。
p.s.這些都是手打的，又Q又有嚼勁。
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Exercise #9
1.p252:4 For which sets A, B is it true that A×B=B×A?
2.p252:12 Let A, B be sets with ∣B∣=3. If there are 4096 relations from
A to B, what is ∣A∣?
3.p364:3 Let (A,R1), (B,R2) be two posets. On A×B, define relation R by
(a,b)R(x,y) if aR1x and bR2y. Prove that R is a partial order.
4.p365:6 For A={a,b,c,d,e}, the Hasse diagram for the poset (A,R) is shown
in Fig. 7.23. (a) Determine the relation matrix for R. (c)
Topologically sort the poset (A,R).
5.p370:8 If A={1,2,3,4,5,6,7}, define R on A by (x, y)屬於R if x-y is a
mutiple of 3.a)Show that R is an equivalence relation
on A.b)Determine the equivalence classes and partition
of A induced by R.
6.p371:14 Let A={1,2,3,4,5,6,7}. For each of the following values of γ,
determine an equivalence relation R on A with ∣R∣=γ, or explain
why no such relation exists.(a)γ=6;(b)γ=7;
(d)γ=9;(f)γ=22.
p.s. R=那扭來扭去的符號。
Fig. 7.23
ｅ
∣
∣d
／＼
b／ ＼c
＼ ／
＼／
ａ
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