# Prove the following relations by Contradiction (Use rules. Don’t use truth table). a) [B ^^ (B rarr C )] rarr C b) not (p vv not (p ∧ q) ) rarr q

Question
Discrete math
Prove the following relations by Contradiction (Use rules. Don’t use truth table).
a) $$\displaystyle{\left[{B}\wedge{\left({B}\rightarrow{C}\right)}\right]}\rightarrow{C}$$
b) $$\displaystyle\neg{\left({p}\vee\neg{\left({p}∧{q}\right)}\right)}\rightarrow{q}$$

2021-01-09

### Relevant Questions

For the following questions you must use the rules of logic (Don’t use truth tables)
a) Show that ($$\displaystyle{p}\leftrightarrow{q}$$) and ($$\displaystyle\neg{p}\leftrightarrow\neg{q}$$ ) are logically equivalent.
b) Show that not ( $$\displaystyle{p}\oplus{q}$$) and ($$\displaystyle{p}\leftrightarrow{q}$$) are logically equivalent.
Use proof by Contradiction to prove that the sum of an irrational number and a rational number is irrational.
Dayton Power and Light, Inc., has a power plant on the Miami Riverwhere the river is 800 ft wide. To lay a new cable from the plantto a location in the city 2 mi downstream on the opposite sidecosts $180 per foot across the river and$100 per foot along theland.
(a) Suppose that the cable goes from the plant to a point Q on theopposite side that is x ft from the point P directly opposite theplant. Write a function C(x) that gives the cost of laying thecable in terms of the distance x.
(b) Generate a table of values to determin if the least expensivelocation for point Q is less than 2000 ft or greater than 2000 ftfrom point P.

When a gas is taken from a to c along the curved path in the figure (Figure 1) , the work done by the gas is W = -40 J and the heat added to the gas is Q = -140 J . Along path abc, the work done by the gas is W = -50 J . (That is, 50 J of work is done on the gas.)
I keep on missing Part D. The answer for part D is not -150,150,-155,108,105( was close but it said not quite check calculations)
Part A
What is Q for path abc?
Express your answer to two significant figures and include the appropriate units.
Part B
f Pc=1/2Pb, what is W for path cda?
Express your answer to two significant figures and include the appropriate units.
Part C
What is Q for path cda?
Express your answer to two significant figures and include the appropriate units.
Part D
What is Ua?Uc?
Express your answer to two significant figures and include the appropriate units.
Part E
If Ud?Uc=42J, what is Q for path da?
Express your answer to two significant figures and include the appropriate units.
(1 pt) A new software company wants to start selling DVDs withtheir product. The manager notices that when the price for a DVD is19 dollars, the company sells 140 units per week. When the price is28 dollars, the number of DVDs sold decreases to 90 units per week.Answer the following questions:
A. Assume that the demand curve is linear. Find the demand, q, as afunction of price, p.
B. Write the revenue function, as a function of price. Answer:R(p)=
C. Find the price that maximizes revenue. Hint: you may sketch thegraph of the revenue function. Round your answer to the closestdollar.
D. Find the maximum revenue. Answer:

A random sample of $$n_1 = 14$$ winter days in Denver gave a sample mean pollution index $$x_1 = 43$$.
Previous studies show that $$\sigma_1 = 19$$.
For Englewood (a suburb of Denver), a random sample of $$n_2 = 12$$ winter days gave a sample mean pollution index of $$x_2 = 37$$.
Previous studies show that $$\sigma_2 = 13$$.
Assume the pollution index is normally distributed in both Englewood and Denver.
(a) State the null and alternate hypotheses.
$$H_0:\mu_1=\mu_2.\mu_1>\mu_2$$
$$H_0:\mu_1<\mu_2.\mu_1=\mu_2$$
$$H_0:\mu_1=\mu_2.\mu_1<\mu_2$$
$$H_0:\mu_1=\mu_2.\mu_1\neq\mu_2$$
(b) What sampling distribution will you use? What assumptions are you making? NKS The Student's t. We assume that both population distributions are approximately normal with known standard deviations.
The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.
(c) What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate.
(Test the difference $$\mu_1 - \mu_2$$. Round your answer to two decimal places.) NKS (d) Find (or estimate) the P-value. (Round your answer to four decimal places.)
(e) Based on your answers in parts (i)−(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level \alpha?
At the $$\alpha = 0.01$$ level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are statistically significant.
At the $$\alpha = 0.01$$ level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are not statistically significant.
(f) Interpret your conclusion in the context of the application.
Reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver. (g) Find a 99% confidence interval for
$$\mu_1 - \mu_2$$.
lower limit
upper limit
(h) Explain the meaning of the confidence interval in the context of the problem.
Because the interval contains only positive numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, we can not say that the mean population pollution index for Englewood is different than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains only negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is less than that of Denver.
A box is sliding with a speed of 4.50 m/s on a horizontal surface when, at point P, it encounters a rough section. On the rough section, the coefficient of friction is not constant but starts at .100 at P and increases linerly with distance past P, reaching a value of .600 at 12.5 m past point P. (a) Use the work energy theorem to find how far this box slides before stopping. (b) What is the coefficient of friction at the stopping point? (c) How far would the box have slid iff the friciton coefficient didn't increase, but instead had the constant value of .1?
Use the rules for derivatives to find the derivative of function defined as follows.
$$\displaystyle{q}={\left({e}^{{{2}{p}+{1}}}-{2}\right)}^{{{4}}}$$
For the following, write your list in increasing order, separated by commas.
a, List the first 10 multiples of 8.
b. LIst the first 10 multiples on 12.
c. Of the lists you produced in parts a. and b., list the multiples that 8 and 12 have in common.
d. From part c., what is the smallest multiple that 8 and 12 have in common.
Hypothetical potential energy curve for aparticle of mass m
If the particle is released from rest at position r0, its speed atposition 2r0, is most nearly
a) $$\displaystyle{\left({\frac{{{8}{U}{o}}}{{{m}}}}\right)}^{{1}}{\left\lbrace/{2}\right\rbrace}$$
b) $$\displaystyle{\left({\frac{{{6}{U}{o}}}{{{m}}}}\right)}^{{\frac{{1}}{{2}}}}$$
c) $$\displaystyle{\left({\frac{{{4}{U}{o}}}{{{m}}}}\right)}^{{\frac{{1}}{{2}}}}$$
d) $$\displaystyle{\left({\frac{{{2}{U}{o}}}{{{m}}}}\right)}^{{\frac{{1}}{{2}}}}$$
e) $$\displaystyle{\left({\frac{{{U}{o}}}{{{m}}}}\right)}^{{\frac{{1}}{{2}}}}$$
if the potential energy function is given by
$$\displaystyle{U}{\left({r}\right)}={b}{r}^{{P}}-\frac{{3}}{{2}}\rbrace+{c}$$
where b and c are constants
which of the following is an edxpression of the force on theparticle?
1) $$\displaystyle{\frac{{{3}{b}}}{{{2}}}}{\left({r}^{{-\frac{{5}}{{2}}}}\right)}$$
2) $$\displaystyle{\frac{{{3}{b}}}{{{2}}}}{\left\lbrace{3}{b}\right\rbrace}{\left\lbrace{2}\right\rbrace}{\left({r}^{{-\frac{{1}}{{2}}}}\right)}$$
3) $$\displaystyle{\frac{{{3}{b}}}{{{2}}}}{\left\lbrace{3}\right\rbrace}{\left\lbrace{2}\right\rbrace}{\left({r}^{{-\frac{{1}}{{2}}}}\right)}$$
4) $$\displaystyle{2}{b}{\left({r}^{{-\frac{{1}}{{2}}}}\right)}+{c}{r}$$
5) $$\displaystyle{\frac{{{3}{b}}}{{{2}}}}{\left\lbrace{2}{b}\right\rbrace}{\left\lbrace{5}\right\rbrace}{\left({r}^{{-\frac{{5}}{{2}}}}\right)}+{c}{r}$$
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