(4 points) Convert each of the following sentences into a symbolic statement. Assume that the universe...

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(4 points) Convert each of the following sentences into a symbolic statement. Assume that the universe set is X = R. a. For every x, there is a y such that x = 2y. b. There exists an z such that g(x) > 0. c. There is a y such that zy = 0 for every 2. d. For all e > 0, there exists a > 0 such that if x is a real number with |x-1| < 6, then |x² − 1| < ɛ. (4 points) Negate each of the symbolic statements from exercise 4.1, and convert them into sentences. Definition 1. (A positive integer p is prime when it has exactly two factors, 1 and p). (4 points) Each of the following statements are false. Give a counterexample for each: a. Every odd number is prime. b. Every prime number is odd. c. For every real number z, we have z² > 0. d. For every real number z # 0, we have 1/2 > 0. (8 points) Prove the following: Let n be an integer. Show that n is odd if and only if 5n+ 4 is odd. (4 points) Convert each of the following sentences into a symbolic statement. Assume that the universe set is X = R. a. For every x, there is a y such that x = 2y. b. There exists an z such that g(x) > 0. c. There is a y such that zy = 0 for every 2. d. For all e > 0, there exists a > 0 such that if x is a real number with |x-1| < 6, then |x² − 1| < ɛ. (4 points) Negate each of the symbolic statements from exercise 4.1, and convert them into sentences. Definition 1. (A positive integer p is prime when it has exactly two factors, 1 and p). (4 points) Each of the following statements are false. Give a counterexample for each: a. Every odd number is prime. b. Every prime number is odd. c. For every real number z, we have z² > 0. d. For every real number z # 0, we have 1/2 > 0. (8 points) Prove the following: Let n be an integer. Show that n is odd if and only if 5n+ 4 is odd.

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solution 4 points Convert each of the following sentences into a symbolic statement Assume that the ... View the full answer