有关中秋节的手抄报-财务预算报告范文

7.4--- 2.令A={1,2,3,4,5,6,7,8},有多少種方法我們可以將A分割為
A
1
∪A
2
∪A
3
,其中
a) 1,2∈A
1
, 3,4∈A
2
,且5,6,7∈A
3
?
b) 1,2∈A
1
, 3,4∈A
2
, 5,6∈A
3
,且|A
1
|=3?
c) 1,2∈A
1
, 3,4∈A
2
,且5,6∈A
3
?
(a) There are three choices for placing 8 – in each
A
1
,A
2
,A
3
. Hence there are three
partitions of A for the conditions given.
(b) There are two possibilities with
7A
1
, Hence there are four partitions of A
under these conditions.
(c) If we place 7, 8 in the same cell for a partition we obtain three of the possibilities.
If not, there are three choices of cells for 7 and two choices of cells for 8 – and
six more partitions that satisfy the stated restrictions. In total – by the rules of
sum and product – there are 3+(3)(2)=3+6=9 such partitions.

7.4---4.對A={1,2,3,4,5,6},R={(1,1), (1,2), (2,1), (2,2), (3,3), (4,4), (4,5),
(5,4), (5,5), (5,6),(6,6)}是A上的一個等價關係. (a)在這個等價關係下,
[1],[2]及[3]是什麼? (b) R引出A的什麼分割?
(a) [1]={1,2} = [2]; [3] = {3}
(b)
A{1,2}{3}{4,5}{6}


7.4---8.
(a) For all
aA
, a-a=3*0, so R is reflexive. For
a,bA
, a-b=3c, for some
czba3(c)
, for
cZ
, so
aRbbRa
and R is symmetric. If
a,b,cA
and aRb bRc, then a-b=3m, b-c=3n, for some
m,nZ(ab)(bc)3m3nac3(mn)
, so aRc. Consequently,
R is transitive.
(b) [1]=[4]=[7]={1,4,7}; [2]=[5]={2,5}; [3]=[6]={3,6}
A{1,4,7}{2,5}{3,6}


7.4--- 12.令A={v,w,x,y,z}. 求A上關係的個數,使得這些關係為

(a)反身及對稱的; (b)等價關係; (c)反身及對稱的但非遞移的;
(d)等價關係且恰決定兩個等價類; (e)等價關係,其中w∈[x];
(f)等價關係,其中v,w∈x; (g)等價關係,其中w∈[x], y∈[z];
(h)等價關係,其中w∈[x], y∈[z],且[x]不等於[z]
(a)
2
10
1024

(b)

5
i1
S(5,i)1152510152

(c) 1024-52=972
(d) S(5,2)=15
(e)
(f)
(g)



4
i1
S(4,i)176115
S(3,i)1315
S(3,i)1315
3
i1
3
i1
3
(h) (

3i1
S(3,i))(

i1
S(2,i))3