Homework Answers
The hypothesis of a conditional statement is the phrase immediately following the word if. The conclusion of a conditional statement is the phrase immediately following the word then.
(a)
Hypothesis: n is a prime number.
Conclusion: n2 has three positive factors.
(b)
Hypothesis: a and b are irrational number.
Conclusion: a.b is an irrational number.
(c)
Hypothesis: p is a prime number.
Conclusion: p = 2 or p is an odd number.
(d)
Hypothesis: p is a prime number and p 2.
Conclusion: p is an odd number.
(e)
Hypothesis: p 2 and p is an even
number.
Conclusion: p is not prime.
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2. Identify the hypothesis and the conclusion for each of the following condi- tional statements. (a)...
Problem3 Prove each of the following statements below a. The product of a nonzero rational number...
Problem3 Prove each of the following statements below a. The product of a nonzero rational number and an irrational number is irrational. b. If n is an integer and n3 +5 is odd, then n is even.
#7. TRUE/FALSE. Determine the truth value of each sentence (no explanation required). ________(a) k in Z k2 + 9 = 0....
#7. TRUE/FALSE. Determine the truth value of each sentence (no explanation required). ________(a) k in Z k2 + 9 = 0. ________(b) m, n in N, 5m 2n is in N. ________(c) x in R, if |x − 2| < 3, then |x| < 5. #8. For each statement, (i) write the statement in logical form with appropriate variables and quantifiers, (ii) write the negation in logical form, and (iii) write the negation in a clearly worded unambiguous English sentence....
1. Answer each of the following statements as true, false, or unknown. a. The set of...
1. Answer each of the following statements as true, false, or unknown. a. The set of nonnegative even integers is well ordered. b. The sequence of Mersenne numbers forms a geometric progression. c. The sequence {na +1} contains infinitely many primes. d. The sequence {n" +1}.contains infinitely many composites. D) - logo) e. The Prime Number Theorem implies that lim ++00 f. There exist infinitely many pairs of primes that differ by less than 300. g. The number V110520191105201911052019 is...
Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final...
Identify the null hypothesis, alternative hypothesis, test
statistic, P-value, conclusion about the null hypothesis, and
final conclusion that addresses the original claim
In a study of 420,089 cell phone users, 120 subjects developed cancer of the brain or nervaus system. Test the claim af a somewhat common belief that such cancers are affected by cell phone use. That is, test the claim that cell phone users develop cancer of the brain or nervous system at a rate that is different...
1.)Which of the expressions is equivalent to the following statement: The sum of two even numbers...
1.)Which of the expressions is equivalent to the following statement: The sum of two even numbers is even. a.) If x is even or y is even, then x + y b.) If x is even or y is even, then x + y is even c.) If x is even and y is even, then x + y is not even. d.) If x is even and y is even, then x + y is even 2.) Find a...
A fair, six-sided die is rolled. Describe the sample space S, identify each of the following...
A fair, six-sided die is rolled. Describe the sample space S, identify each of the following events with a subset of S and compute its probability (an outcome is the number of dots that show up). a. Event T = the outcome is three. b. Event A = the outcome is an odd number c. Event B = the outcome is less than four. d. Event D = the complement of A e. A AND B f. A OR B...
a. Define what it means for two logical statements to be equivalent b. If P and Q are two statements, show that the statement ( P) л (PvQ) is equivalent to the statement Q^ P c. Write the converse a...
a. Define what it means for two logical statements to be equivalent b. If P and Q are two statements, show that the statement ( P) л (PvQ) is equivalent to the statement Q^ P c. Write the converse and the contrapositive of the statement "If you earn an A in Math 52, then you understand modular arithmetic and you understand equivalence relations." Which of these d. Write the negation of the following statement in a way that changes the...
Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final...
Identify the null hypothesis,
alternative hypothesis, test statistic, P-value, conclusion about
the null hypothesis, and final conclusion that addresses the
original claim. Use the P-value method. Use the normal
distribution as an approximation of the binomial distribution.
7. In a recent poll of 745 randomly selected adults, 585 said that it is morally wrong to not report all income on tax returns. Use a 0.01 significance level report all income on tax returns. Identify the null hypothesis, altemative hypothesis, test...
Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final...
Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method. Use either the T Calculator or the Normal Calculator to compute the P-value of the following test statistics. (a) The test statistic in a two-tailed is z = 1.39. Round to four decimal places. (b) Find the P-value for a right-tailed test with n = 27 and test statistic t = 1.502. Round to...
Question 3 (a) Write down the prime factorization of 10!. (b) Find the number of positive...
Question 3 (a) Write down the prime factorization of 10!. (b) Find the number of positive integers n such that n|10! and gcd(n, 27.34.7) = 27.3.7. Justify your answer. Question 4 Let m, n E N. Prove that ged(m2, n2) = (gcd(m, n))2. Question 5 Let p and q be consecutive odd primes with p < q. Prove that (p + q) has at least three prime divisors (not necessarily distinct).
Problem3 Prove each of the following statements below a. The product of a nonzero rational number and an irrational number is irrational. b. If n is an integer and n3 +5 is odd, then n is even.
1. Answer each of the following statements as true, false, or unknown. a. The set of nonnegative even integers is well ordered. b. The sequence of Mersenne numbers forms a geometric progression. c. The sequence {na +1} contains infinitely many primes. d. The sequence {n" +1}.contains infinitely many composites. D) - logo) e. The Prime Number Theorem implies that lim ++00 f. There exist infinitely many pairs of primes that differ by less than 300. g. The number V110520191105201911052019 is...
Identify the null hypothesis, alternative hypothesis, test
statistic, P-value, conclusion about the null hypothesis, and
final conclusion that addresses the original claim
In a study of 420,089 cell phone users, 120 subjects developed cancer of the brain or nervaus system. Test the claim af a somewhat common belief that such cancers are affected by cell phone use. That is, test the claim that cell phone users develop cancer of the brain or nervous system at a rate that is different...
a. Define what it means for two logical statements to be equivalent b. If P and Q are two statements, show that the statement ( P) л (PvQ) is equivalent to the statement Q^ P c. Write the converse and the contrapositive of the statement "If you earn an A in Math 52, then you understand modular arithmetic and you understand equivalence relations." Which of these d. Write the negation of the following statement in a way that changes the...
Identify the null hypothesis,
alternative hypothesis, test statistic, P-value, conclusion about
the null hypothesis, and final conclusion that addresses the
original claim. Use the P-value method. Use the normal
distribution as an approximation of the binomial distribution.
7. In a recent poll of 745 randomly selected adults, 585 said that it is morally wrong to not report all income on tax returns. Use a 0.01 significance level report all income on tax returns. Identify the null hypothesis, altemative hypothesis, test...
Question 3 (a) Write down the prime factorization of 10!. (b) Find the number of positive integers n such that n|10! and gcd(n, 27.34.7) = 27.3.7. Justify your answer. Question 4 Let m, n E N. Prove that ged(m2, n2) = (gcd(m, n))2. Question 5 Let p and q be consecutive odd primes with p < q. Prove that (p + q) has at least three prime divisors (not necessarily distinct).
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