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s feud with Nezha over his son39。s recall these colorful images that brought the country great joy. Calabash Brothers Calabash Brothers (Chinese: 葫蘆娃 ) is a Chinese animation TV series produced by Shanghai Animation Film Studio. In the 1980s the series was one of the most popular animations in China. It was released at a point when the Chinese animation industry was in a relatively downed state pared to the rest of the international munity. Still, the series was translated into 7 different languages. The episodes were produced with a vast amount of papercut animations. Black Cat Detective Black Cat Detective (Chinese: 黑貓警長 ) is a Chinese animation television series produced by the Shanghai Animation Film Studio. It is sometimes known as Mr. Black. The series was originally aired from 1984 to 1987. In June 2021, a rebroadcasting of the original series was announced. Critics bemoan the series39。 13. 證明當(dāng)且僅當(dāng) G 的一條邊 e 不包含在 G 的回路中時(shí), e 才是 G 的割邊。 8. 設(shè) f: XY 和 g: YZ 是函數(shù),使得 g?f 是一個(gè)滿射,且 g是一個(gè)入射。 16. 下圖給出的賦權(quán)圖表示五個(gè)城市及對(duì)應(yīng)兩個(gè)城鎮(zhèn)間公路的長度。 8. 以下哪些是函數(shù)?哪些是入射?哪些是滿射?對(duì)任意一個(gè)雙射,寫出它們的逆函數(shù)。 ( 2)某些 教練是年老的,但是健壯的。 13. 一棵樹有 n2個(gè)結(jié)點(diǎn)度數(shù)為 2, n3個(gè)結(jié)點(diǎn)度數(shù)為 3,??, nk個(gè)結(jié)點(diǎn)度數(shù)為 k,則度數(shù)為 1 的結(jié)點(diǎn)的個(gè)數(shù)為 。則公式 (?x)(?y)(P(x,y)?P(y,x))的真值是 。 19. ( )任意平面圖最多是四色的。如果該代數(shù)系統(tǒng)中存在幺元 e 和零元 ?,則 e??。 4. ( ) A、 B、 C 是任意命題公式,如果 A?C?B?C,一定有 A?B。 5. ( )若集合 A上的二元關(guān)系 R是對(duì)稱的, RC一定是對(duì)稱的。 12. ( ) 交換群必是循環(huán)群。 20. ( )不存在既有歐拉回路又有漢密爾頓回路的圖。 5. 集合 A={?,{?}}的冪集 P(A)為 6. 集合 A={1,2}, B={a,b,c,d}, C={c,d,e},則 A?(BC)為 7. 試用空集 ?構(gòu)成集合 A( A??) = 和 B= ,使得 A?B 且 A?B 都成立。 14. 設(shè) T 為根樹,若每個(gè)結(jié)點(diǎn)的出度都小 于等于 m,則 T 稱為 樹,若除 外,每個(gè)結(jié)點(diǎn)的出度都等于 m,則 T 稱為完全 m 叉樹。 ( 3)任何自然數(shù)不是偶數(shù)就是奇數(shù) 。 a) f: Z?N, f(x)=x2+1 b) f: N?Q, f(x) = 1/x c) f: {1,2,3}?{a,b,c}, f={1,b,2,c,3,a} d) f: N?N, f(x)=2x e) f: R?R?R?R, f(x,y)=y+1,x+1 9. 設(shè) S={1,2,3,4,6,12}, D為 S上的整除關(guān)系, ( 1)試寫出該關(guān)系并畫出哈斯圖; ( 2)設(shè)子集 B={2,3,6},試求 B的最大元、最小元、極大元和極小元; ( 3)試求 B的上界、 上確界、下界和下確界。是給出一個(gè)最優(yōu)的設(shè)計(jì)方案使各城市間有公路連通。證明 f 是滿射。 14. 畫出 K3,3 圖,并證明其不是歐拉圖,也不是平面圖。 violence, and lack of suitability for children39。s death. Through bravery and wit, Nezha finally broke into the underwater palace and successfully defeated him. The film shows various kinds of attractive sceneries and the traditional culture of China, such as spectacular mountains, elegant sea waves and exquisite ancient Chinese clothes. I