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Assignment.3.Solutions.cs2101

# Assignment.3.Solutions.cs2101 - Assignment 3 Solutions...

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Assignment 3 Solutions CS2102, Fall 2009 1. (2.1, 1) Answer: 1a. False Explanation: Symbolically, for the menagerie set of animals M , the statement is M x : color(x) = red. Because there are no animals in the menagerie that are red, this statement is false. Answer: 1b. True Explanation: Because the menagerie consists of dogs, cats, and birds, then each animal is either a bird or a mammal. Symbolically, this statement would be M x : bird(x) mammal(x) Answer: 1c. False. Explanation: There are some animals in the menagerie that are not black, gray, or brown. Therefore the statement that every animal is of one of these three colors is false. Symbolically, this statement is M x : black(x) grey(x) brown(x). Answer: 1d. True Explanation: There is a bird in the menagerie. A bird is not a dog or a cat. Therefore the statement that there is an animal in the menagerie that is not a dog or a cat is true. Symbolically, the statement is M x : ¬dog(x) ¬cat(x). Answer: 1e. False Explanation: There are 5 blue birds in the menagerie. Therefore the statement that no animal in the menagerie is blue must be false. Symbolically this statement is M x : ¬blue(x) Answer: 1f. True Explanation: The menagerie has 2 black dogs, ten black cats, and one black bird. Therefore there are a dog, cat, and bird in the menagerie that all have the same color. Symbolically, this is M z y x : , , | dog(x) ^ cat(y) ^ bird(z) (color(x) = color(y) = color(z)). 2. (2.1, 6) Answer/Explanation: 6a. If m= 25 and n = 10, The predicate reads “If 25 is a factor of 100, then 25 is a factor of 10”. 25 is a factor of 100, but it is not a factor of 10. Therefore, the statement is false for these m and n values (recall 1 0 = 0). Answer: 6b. n =100 , m = 2500 Explanation: Any set of values where m is a factor of n 2 but m is not a factor of n is an acceptable answer here.

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Answer/Explanation: 6c. If m = 5 and n = 10, then the predicate reads “If 5 is a factor of 100, then 5 is a factor of 10”. 5 is a factor of 100, and 5 is a factor of 10. Since both parts of the statement are true, the statement is true (recall 1 1 = 1). Answer: 6d. n = 4, m = 2, or n = 5, m = 3. Explanation: Any n and m values where m is a factor of n 2 and n will make the statement true. Also, the statement will be true for any value where m is not a factor of n 2 , regardless of whether or not m is a factor of n. Recall that 1 1 = 1 and 0 1 = 1 and 0 0 = 1. 3. (2.1, 10) Answer: If a = 1, the statement is false. Explanation: The statement says that for every integer a, (a - 1)/a is not an integer. To show that the statement is false, we only need to find one integer a where (a – 1)/a is an integer. If a = 1, (a - 1)/a = (1 – 1)/1 = 0. 0 is an integer, so this is a valid counterexample to prove that the statement is false. 4.
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Assignment.3.Solutions.cs2101 - Assignment 3 Solutions...

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