Assignment 2 Solutions

# Assignment 2 Solutions - Assignment#2 Due Tuesday 1/27...

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Assignment #2 Due Tuesday, 1/27 Complete the following exercises from chapter 1.3: 2, 8, 10 Complete the following exercises from chapter 1.4: d 14, 28, 32(a,b, and d) Complete the following exercises from chapter 1.5: 14, 24 For question 14, translate the arguments to mathematical symbols and do two-column proofs in the style of examples 12 and 13 on page 71 Points assigned 1.4.14 gets 20 points 1.5.14 gets 20 points Each remaining problem gets 10 points Chapter 1.3 Exercise 2: Let P(x) be the statement “the word x contains the letter a.” What are the truth values for the following? Chapter 1.3 Exercise 8: Translate these statements into English, where R(x) is “x is a rabbit” and H(x) is “x hops” and the domain consists of all animals. a) 2200 x(R(x) H(x)) b) 2200 x(R(x) H(x)) c) 5 x(R(x) H(x)) d) 5 x(R(x) H(x)) Part Statement truth value a P(orange) T b P(lemon) F c P(true) F d P(false) T Part Statement English Sentence a 2200 x(R(x) H(x)) If an animal is a rabbit, then that animal hops. Alternatively, every rabbit hops. b 2200 x(R(x) H(x)) Every animal is a rabbit and hops. Alternatively, every animal is hopping rabbit. Alternatively, every animal is a rabbit that hops. c 5 x(R(x) H(x)) There exists an animal such that if it is a rabbit, then it hops. d 5 x(R(x) H(x)) There exists an animal that is a rabbit and hops. Alternatively, some rabbits hop. Alternatively, some hopping animals are rabbits.

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Chapter 1.3 Exercise 10: Let C(x) be the statement “x has a cat,” D(x) be the statement “x has a dog,” and F(x) be the statement “x has a ferret.” Express each of these statements in terms of C(x), D(x), and F(x), quantifiers, and logical connectives. Let the domain consist of all students in your class. Chapter 1.4 Exercise 14: 20 points
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Assignment 2 Solutions - Assignment#2 Due Tuesday 1/27...

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