高分求助：关于离散数学的逻辑谓词问题，简单。急在线等。。英文翻译过来的，肯能有点不标准。谢谢了。

Question

1.D(x),F(x)分别代表：“x是一只狗”和“x是毛皮”。A代表所有的动物。
求用逻辑谓词翻译下列句子：“不是所有狗都是皮毛”和“有一些狗不是皮毛”
2.现有如下谓词：
g(x,y): x大于y
e(x,y):x=y
sum(x,y,z):x+y=z
prod(x,y,z):x的y倍等于z。
和定义域 自然数N。
翻译一下句子：
a) 所有5的倍数大于7。
b)存在一个奇数的自然数。
c)任意自然数相加是可交换的。
d)不是所有的自然数都是2的倍数。
3.用逻辑谓词翻译一下句子：并证明或者反驳该陈诉。
a）存在三个非零整数，前两个的平方和和等于第三个的平方。
b）存在三个非零整数，前两个的立方和等于第三个的立方。

Answer 1

1.D ( x ), F ( x ) represent respectively:" x is a dog" and" x is fur". The A represents all the animal.
Ask use logic predicate to translate the following sentence:" not all dogs are fur" and" some dog 's fur"
2 the following predicate:
G ( x, y ): x greater than y
E ( x, y ): x = y
Sum ( x, y, z ): x+y = Z
Prod ( x, y, z ): x y is equal to Z times.
And defining the domain of natural number N.
Translate the sentence:
A ) all multiples of 5 is greater than 7.
B ) has an odd number of natural number.
C ) arbitrary natural number addition is commutative.
D ) not all natural numbers are multiples of 2.
3 logical predicates and translate the sentence: to prove or disprove the report.
A ) the existence of three non-zero integer, the first two of the square and the square is equal to third.
B ) the existence of three non-zero integer, the first two cubic and equal to third cubic.

Answer 2

看

1.D ( x ), F ( x ) represent respectively:" x is a dog" and" x is fur". The A represents all the
animal.
Ask use logic predicate to translate the following sentence:" not all dogs are fur" and" some dog 's fur"
2 the following predicate:
G ( x, y ): x greater than y
E ( x, y ): x = y
Sum ( x, y, z ): x+y = Z
Prod ( x, y, z ): x y is equal to Z times.
And defining the domain of natural number N.
Translate the sentence:
A ) all multiples of 5 is greater than 7.
B ) has an odd number of natural number.
C ) arbitrary natural number addition is commutative.
D ) not all natural numbers are multiples of 2.
3 logical predicates and translate the sentence: to prove or disprove the report.
A ) the existence of three non-zero integer, the first two of the square and the square is equal to third.
B ) the existence of three non-zero integer, the first two cubic and equal to third cubic.