發布者 | 內容列 | 訪客
| 請問離散學數的問題二則????? | | 第一題: Let A ={1,2,3,4}and B={a,b,c,d,e}.Let f:A→B be defined by f={(1,d),(2,e),(3,d),(4,b)} and g:B→A {(a,2),(b,1),(c,3),(d,1),(e,4)}.List the ordered paris in f。g and g。f .
第二題: Let R be the relation on Z*N defined by (a,b) R (c,d) if ad=bc,then prove that R is an equivalence relation.
麻煩各位高手了.......謝謝 |
| 2002-10-20 18:33 | | 訪客
| Re: 請問離散學數的問題二則????? | | In First Problem: The function f。g :B -->B and g。f : A -->A thus, f。g={(a,e), (b,d), (c,d), (d,d), (e,b)} Try g。f yourself!
The Second Proiblem: Let R be the relation on Z*N defined by (a,b) R (c,d) if ad=bc,then prove that R is an equivalence relation.
Proof: 1. since aa=aa, => (a,a) R (a,a) for (a,a) in Z*N 2. If (a,b) R (c,d) then ad=bc => bc=ad, thus (a,b) R (c,d). 3. If (a,b) R (c,d), and (c,d) R (e,f), for all of them are in Z*N, then we have ad=bc and de=cf, since af=ade/c = bce/c = be, thus (a,b) R (e,f).
by 1.~3. we have prove that the Relation R is an equi. relation on Z*N.
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| 2002-10-22 09:42 | |
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