20春学期《离散数学X》在线平时作业2

adminhan · 发表于 2020-8-8 19:01:01

单选填空题。E是全集，E={a,b}，E的幂集P(E)上的交运算<span lang="EN-US" style="FONT-FAMILY: Symbol; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-weight: bold; mso-char-type: symbol; mso-symbol-font-family: Symbol">Ç的有逆元的元素是（         ）。
A:Φ； 
B: {a} ；    
C:{b}；    
D: {a,b}； 
E:不存在。<o:p></o:p>

<img src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257793747341.bmp"></img>
A:<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257794101562.bmp"></img>
B:<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257794423593.bmp"></img>
C:<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257794637964.bmp"></img>
D:<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257794850315.bmp"></img>

下面是<o:p></o:p><span lang="EN-US" style="FONT-FAMILY: Symbol; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-size: 10.5pt; mso-char-type: symbol; mso-symbol-font-family: Symbol; mso-bidi-font-weight: bold">"xC(x),  <span lang="EN-US" style="FONT-FAMILY: Symbol; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-size: 10.5pt; mso-char-type: symbol; mso-symbol-font-family: Symbol; mso-bidi-font-weight: bold">$x(A(x)<span lang="EN-US" style="FONT-FAMILY: Symbol; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-size: 10.5pt; mso-char-type: symbol; mso-symbol-font-family: Symbol; mso-bidi-font-weight: bold">ÚB(x)),   <span lang="EN-US" style="FONT-FAMILY: Symbol; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-size: 10.5pt; mso-char-type: symbol; mso-symbol-font-family: Symbol; mso-bidi-font-weight: bold">"x(B(x)<span lang="EN-US" style="FONT-FAMILY: Symbol; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-size: 10.5pt; mso-char-type: symbol; mso-symbol-font-family: Symbol; mso-bidi-font-weight: bold">®<span lang="EN-US" style="FONT-FAMILY: Symbol; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-size: 10.5pt; mso-char-type: symbol; mso-symbol-font-family: Symbol; mso-bidi-font-weight: bold">ØC(x))  <span lang="EN-US" style="FONT-FAMILY: Symbol; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-size: 10.5pt; mso-char-type: symbol; mso-symbol-font-family: Symbol; mso-bidi-font-weight: bold">Þ <span lang="EN-US" style="FONT-FAMILY: Symbol; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-size: 10.5pt; mso-char-type: symbol; mso-symbol-font-family: Symbol; mso-bidi-font-weight: bold">$xA(x)<o:p></o:p>的谓词推理过程。在这个过程中每一步中的（  ）处是此步所用的推理规则。请写出这些推理规则。<o:p></o:p>⑴ <span lang="EN-US" style="FONT-FAMILY: Symbol; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-size: 10.5pt; mso-char-type: symbol; mso-symbol-font-family: Symbol; mso-bidi-font-weight: bold">$x(A(x)<span lang="EN-US" style="FONT-FAMILY: Symbol; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-size: 10.5pt; mso-char-type: symbol; mso-symbol-font-family: Symbol; mso-bidi-font-weight: bold">ÚB(x)),      (    )<o:p></o:p>⑵ A(a)<span lang="EN-US" style="FONT-FAMILY: Symbol; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-size: 10.5pt; mso-char-type: symbol; mso-symbol-font-family: Symbol; mso-bidi-font-weight: bold">ÚB(a)              (    )  ⑴<o:p></o:p>⑶ <span lang="EN-US" style="FONT-FAMILY: Symbol; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-size: 10.5pt; mso-char-type: symbol; mso-symbol-font-family: Symbol; mso-bidi-font-weight: bold">"xC(x)                   (    )    ⑷ C(a)                        (     )  ⑶  <o:p></o:p>⑸ <span lang="EN-US" style="FONT-FAMILY: Symbol; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-char-type: symbol; mso-symbol-font-family: Symbol; mso-bidi-font-weight: bold">"x(B(x)→<span lang="EN-US" style="FONT-FAMILY: Symbol; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-char-type: symbol; mso-symbol-font-family: Symbol; mso-bidi-font-weight: bold">ØC(x))    (    ) <o:p></o:p>⑹ B(a)→<span lang="EN-US" style="FONT-FAMILY: Symbol; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-char-type: symbol; mso-symbol-font-family: Symbol; mso-bidi-font-weight: bold">ØC(a)          (    )  ⑸<o:p></o:p>⑺ <span lang="EN-US" style="FONT-FAMILY: Symbol; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-char-type: symbol; mso-symbol-font-family: Symbol; mso-bidi-font-weight: bold">ØB(a)                      (    )  ⑷ ⑹ I12<o:p></o:p>⑻ A(a)                        (    )  ⑵ ⑺ I10<o:p></o:p>⑼ <span lang="EN-US" style="FONT-FAMILY: Symbol; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-char-type: symbol; mso-symbol-font-family: Symbol; mso-bidi-font-weight: bold">$xA(x))                   (    )   ⑻<o:p></o:p>
A:⑴ P；⑵ T； ⑶ T；⑷ UG；⑸ P；⑹ US；⑺ P；⑻ T；⑼ ES。<o:p></o:p>
B:   ⑴ P；⑵ EG；⑶ T；⑷ UG；⑸ P；⑹ UG；⑺ P；⑻ T；⑼ EG。<o:p></o:p>
C:   ⑴ P；⑵ ES；⑶  P；⑷ US；⑸ P；⑹ US；⑺ T；⑻ T；⑼ EG。<o:p></o:p>
D:  ⑴ P；⑵ US；⑶ T；⑷ UG；⑸ P；⑹ UG；⑺ P；⑻ T；⑼ UG。

<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257656827651.bmp"></img>
A:<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257657027962.bmp"></img>
B:<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257657182653.bmp"></img>
C:<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257657315624.bmp"></img>
D:<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257657514535.bmp"></img>

单选填空题：对于自然数集合N上的加法运算“＋”，13＝（          ）。
A: 0；
B:1；
C:3； 
D:6。<o:p></o:p>

 设命题P、Q所代表的意义如下：P：天气好。Q：我去旅游。命题“只有天气好，我才去旅游。”的符号表达式为：（         ） 
A:<span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">P<span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: Symbol; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-bidi-font-family: 'Times New Roman'; mso-char-type: symbol; mso-symbol-font-family: Symbol">®<span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">Q<span style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-bidi-font-family: 'Times New Roman'">，
B:<span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">Q<span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: Symbol; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-bidi-font-family: 'Times New Roman'; mso-char-type: symbol; mso-symbol-font-family: Symbol">®<span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"> P<span style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-bidi-font-family: 'Times New Roman'">，
C:<span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: Symbol; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-bidi-font-family: 'Times New Roman'; mso-char-type: symbol; mso-symbol-font-family: Symbol">Ø<span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"> P <span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: Symbol; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-bidi-font-family: 'Times New Roman'; mso-char-type: symbol; mso-symbol-font-family: Symbol">®<span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"> Q<span style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-bidi-font-family: 'Times New Roman'">，
D:<span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: Symbol; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-bidi-font-family: 'Times New Roman'; mso-char-type: symbol; mso-symbol-font-family: Symbol">Ø<span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"> Q <span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: Symbol; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-bidi-font-family: 'Times New Roman'; mso-char-type: symbol; mso-symbol-font-family: Symbol">®<span lang="EN-US" style="FONT-SIZE: 10.5pt; FONT-FAMILY: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"> P 

选择填空题。R是A上关系，如果R是自反的，当且仅当 （         ）。
A:A中有些元素x，有<x,x>∈R ；
B:所有A中元素x，都有<x,x>∈R ；   
C:所有A中元素x,y，如果有<x,y>∈R ，也有< y, x >∈R；则x=y 。

<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12263081901091.bmp"></img>
A:f是满射，g是入射。
B:f是双射，g是双射
C:f是入射，g是满射。
D:f是入射，g是入射。

<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257662070001.bmp"></img>
A:<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257662257182.bmp"></img>
B:<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257662635783.bmp"></img>
C:<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257663253904.bmp"></img>
D:<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257663473905.bmp"></img>

<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257665293281.bmp"></img>
A:自然数集合
B:整数集合
C:有理数集合
D:实数集合

下面的命题公式中哪些是永真式，只写出题号即可<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123062290326512.bmp"></img>
A:1
B:2
C:3
D:4

试题见图片<span style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-bidi-font-size: 12.0pt"><v:group id="_x0000_s1026" style="MARGIN-TOP: 57.15pt; Z-INDEX: 1; LEFT: 0px; MARGIN-LEFT: 118.5pt; WIDTH: 333pt; POSITION: absolute; HEIGHT: 132.85pt; TEXT-ALIGN: left" coordsize="6660,2657" coordorigin="2340,4135"> <v:shapetype id="_x0000_t202" coordsize="21600,21600" path="m,l,21600r21600,l21600,xe" o:spt="202"><v:stroke joinstyle="miter"></v:stroke><v:path o:connecttype="rect" gradientshapeok="t"></v:path></v:shapetype><v:shape id="_x0000_s1027" style="LEFT: 2520px; WIDTH: 600px; POSITION: absolute; TOP: 5028px; HEIGHT: 425px" stroked="f" fillcolor="#0c9" filled="f" type="#_x0000_t202"><v:textbox style="mso-next-textbox: #_x0000_s1027"><table cellspacing="0" cellpadding="0" width="100%"><tbody><tr><td style="BORDER-RIGHT: #ece9d8; 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A:a 图
B:b图
C:c图
D:d图
E:e图
F:f图
G:g图
H:h图
I:i图
J:j图

多选题。令P(E)是全集E的幂集；Ç是集合的交运算；È是集合的并运算；Å是集合的对称差运算。下面所列代数系统哪些是半群？<o:p></o:p>
A:<P(E),Ç >,  
B:< P(E), È>,   
C:<P(E), Å>。<o:p></o:p>

<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123062356992111.bmp"></img>
A:A：⑴⑵⑶
B:B：⑴⑵⑷
C:C：⑵⑶⑷
D:D：⑴⑵⑶⑷

 多选题。令P(E)是全集E的幂集；Ç是集合的交运算；È是集合的并运算；Å是集合的对称差运算。下面所列代数系统哪些是独异点？<o:p></o:p>
A:<P(E),Ç >, 
B:  < P(E), È>,  
C: <P(E), Å>。<o:p></o:p>

R是A上关系，判断下面命题的真值。<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123069185339013.bmp" />
A:错误
B:正确

R和S都是A上关系，判断下面命题的真值<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123069141981212.bmp" />
A:错误
B:正确

R是A上关系，判断下面命题的真值。<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123069173734311.bmp" />
A:错误
B:正确

设A={a,{a},{a,b},{{a,b},c}}，判断下面命题的真值。<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123068840920313.bmp" />
A:错误
B:正确

判断下面命题的真值<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123068778675011.bmp" />
A:错误
B:正确

R和S都是A上关系，判断下面命题的真值<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123069136082811.bmp" />
A:错误
B:正确

判断下面命题的正误“不是所有完全图Kn都是欧拉图，但是所有完全图Kn都是汉密尔顿图。”
A:错误
B:正确

设A={a,{a},{a,b},{{a,b},c}}，判断下面命题的真值。<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123068820410911.bmp" />
A:错误
B:正确

判断下面命题的真值。<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123068960454614.bmp" />
A:错误
B:正确

判断下面命题的真值<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123068787532812.bmp" />
A:错误
B:正确

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20春学期《离散数学X》在线平时作业2

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