Exercise 4.8. For each of the following, state whether it is true or false. If true,...

Exercise 4.8. For each of the following, state whether it is true or false. If

true, prove. If false, provide a counterexample.
(i) LetX beasetfromRn. ThesetX isclosedifandonlyifX isconvex.

(ii) Let X and Y be sets from Rn. If X ∩Y is closed and convex then Xand Y are both closed and convex sets.

(iii) LetX beanopensetandY ⊆X. IfY ≠∅,thenY isaconvexset.

(iv) SupposeX isanopensetandY isaconvexset. IfX∩Y ⊂X then

X∪Y isopen.

Expert Solution

Colby Messinger answered 2 years ago

State whether EACH of the following statements are true or false. A. A fraction A of...

State whether EACH of the following statements are true or false. A. A fraction A of the Sun’s radiation gets reflected off the atmosphere. (T/F) B. The Earth surface radiates both visible and infrared radiation. (T/F) [ C. Most of the visible radiation from the sun is absorbed by the atmosphere. (T/F) D. The atmosphere emits thermal infrared radiation. (T/F) E. The greenhouse effect is due to the thermal...

For each of the following, state whether True or False: If you repurchase stock at an...

For each of the following, state whether True or False: If you repurchase stock at an amount less than its original issue price, you can record a gain. If you repurchase stock and then reissue it at a higher price, you can record a gain. Interest expense is computed using the effective rate of interest, not the stated rate. Cash interest paid is computed using the stated rate of interest, not the effective rate. Non-interest-bearing notes payable have no interest...

A1.State whether each of the following is true or false. If false, explain why: a.In C++...

A1.State whether each of the following is true or false. If false, explain why: a.In C++ the operator for raising to a power has lower precedence than the multiplication operator b.In C++ the statement x = y = x = 0; is illegal. c.In C++ the expression x < y < z is illegal. d.In C++ the expression x <= y = z is legal. A2.Consider the following program: void main() { enum direction { EAST, WEST, NORTH, SOUTH };...

For each of the following statements, state whether you think the statement is true, false, or...

For each of the following statements, state whether you think the statement is true, false, or uncertain; and explain your answer. If an individual holds a whole-life insurance policy, it is not necessary to monitor the policy periodically. If the stock market is efficient, the best strategy is buy and hold for the long term. A young person should always buy term insurance and not whole-life insurance.

1. State whether each of the following are true or false. A thermodynamic property is always...

1. State whether each of the following are true or false. A thermodynamic property is always conserved. Internal energy change is not dependent on choice of system. Enthalpy change is path dependent. Volume change is not path dependent. Sum of heat and work is path dependent. Reversible work is path dependent. Temperature is constant for an ideal gas if internal energy is constant. Temperature is constant for an ideal gas if entropy is constant. It is possible to convert work...

3. (14) State whether each of the following is True or False. a. A smaller sample...

3. (14) State whether each of the following is True or False. a. A smaller sample could provide less sampling error than a larger sample from a given population. b. The correct critical value a lower tail hypothesis test when sigma is unknown, the sample size = 15, and alpha = 0.05 is -1.645. c. A larger sample size can reduce the potential for extreme sampling error. d. It is impossible for the population mean to equal the mean of...

Please state whether each of the following statements is TRUE or FALSE, and then explain your...

Please state whether each of the following statements is TRUE or FALSE, and then explain your choice briefly. Please start your answer by writing either TRUE or FALSE. Answers without that clear statement at the beginning, and with excessively long (more than 2-3 short sentences) explanations will be penalized. Banks can still influence the money supply if they are required to hold all deposits in reserve. In the months of November and December, people in the U.S. hold a larger...

State whether the following statements are true of false. If they are true, give a short...

State whether the following statements are true of false. If they are true, give a short justification. If they are false, give a counterexample. For each of the following, P(x) is a polynomial. (a) If P(x) has only even powers, and P(a) = 0 then x^2 ? a^2 divides P(x). (b) If P(x) has only odd powers, and P(a) = 0 then x^2 ? a^2 divides P(x). (c) If P(x) has only even powers, then P(x) has at least one...

QUESTION 4 State whether each of the following are TRUE or FALSE, and explain your reasoning...

QUESTION 4 State whether each of the following are TRUE or FALSE, and explain your reasoning for the answer: The binomial distribution is defined by its mean and standard deviation. As the sample size increases, the standard error of the mean decreases. If the population distribution is unknown, in most cases the sampling distribution of the mean can be approximated by the normal distribution if the samples contain at least 10 observations. (b) Suppose the following trend line and seasonal...

B. Theorems--True or False? For each proposition, considered independently: (a) State whether True or False. (b)...

B. Theorems--True or False? For each proposition, considered independently: (a) State whether True or False. (b) Then explain your answer. Define the important terms in your explanation. You may use graphs in your answers. B1. A country's potential output can increase while its actual output decreases. B2. China will likely surpass the United States in per-capita GDP before it surpasses the United States in GDP itself.

Question