Question

In: Advanced Math

3. For each of the English statements below, do the following: i. Define propositions as necessary,...

3. For each of the English statements below, do the following:
i. Define propositions as necessary,
ii. Write the symbolic notation for the implication,
iii. Write the symbolic notation for the inverse then write in English,
iiii. Write the symbolic notation for the contrapositive then write in English.
Note: The sentences should be written in a form consistent with the original sentence. So for instance if the original sentence begins with ‘It is necessary’ the other sentences should begin with ‘It is necessary’ as well. Simplifications should be made if possible.
a) Being a right triangle is sufficient for having three sides and being a polygon.
b) It is necessary for a student to complete assignments and attend class to do well in CSE 2321.

Solutions

Expert Solution

Propositions.

Statement : If p, then q.

Inverse : If not p, then not q.

Contrapositive : If not q, then not p.

Statement : Being a right triangle is sufficient for having three sides and being a polygon.

A is right triangle => A has 3 sides and A is a polygon.

Inverse : A is not a right triangle => A does not have 3 sides or A is not a polygon.

Not being a right triangle is sufficient for either not having 3 sides or not being a polygon.

Contrapositive : A does not have 3 sides or A is not polygon => A is not a triangle.

Not being a polygon or not having 3 sides is sufficient for not being a triangle.

Statement : It is necessary for a student to complete assignments and attend class to do well in CSE 2321.

A student does well in CSE 2321 => He complete assignments and attend classes.

Inverse : A student does not do well in CSE 2321 => He does not complete assignments or he doesn't attend classes.

It is necessary for a student to either bunk classes or not completing assignments to do bad in CSE 2321

Contrapositive : A student does not complete assignments or does not attend classes => He doesn't do well in CSE 2321

Colby Messinger answered 1 year ago
Next > < Previous

Related Solutions

1.Logical equivalence of two English statements. Define the following propositions: j: Sally got the job. l:...
1.Logical equivalence of two English statements. Define the following propositions: j: Sally got the job. l: Sally was late for her interview r: Sally updated her resume. Express each pair of sentences using a logical expression. Then prove whether the two expressions are logically equivalent. (a) If Sally did not get the job, then she was late for interview or did not update her resume. If Sally updated her resume and was not late for her interview, then she got...
Each of the following statements is false or at least misleading. Use M&M propositions to explain...
Each of the following statements is false or at least misleading. Use M&M propositions to explain why in each case. (a) “As the firm borrows more and debt becomes risky, both stockholders and bondholders demand higher rates of return. Thus by reducing the debt ratio we can reduce both the cost of debt and the cost of equity, making everybody better off.” (b) “Moderate borrowing doesn't significantly affect the probability of financial distress or bankruptcy. Consequently, moderate borrowing won't increase...
State whether each of the following six propositions is true or false. In 2-3 sentences, explain...
State whether each of the following six propositions is true or false. In 2-3 sentences, explain why. Use diagrams if helpful. a. Suppose the government passes a law requiring “profit-sharing”; every year, firms must give at least 50% of their profits to their workers. T, F, and Explain: As long as wages are flexible, wages will fall, leaving workers’ well-being unchanged. b. T, F, and Explain: With a volunteer army, wars are bad for taxpayers. With conscription, wars are bad...
State whether each of the following six propositions is true or false. In 2-3 sentences, explain...
State whether each of the following six propositions is true or false. In 2-3 sentences, explain why. Use diagrams if helpful. a. Suppose the government passes a law requiring “profit-sharing”; every year, firms must give at least 50% of their profits to their workers. T, F, and Explain: As long as wages are flexible, wages will fall, leaving workers’ well-being unchanged. b. T, F, and Explain: With a volunteer army, wars are bad for taxpayers. With conscription, wars are bad...
Provide a discussion on each of the following topics. When necessary, define the term, explain the...
Provide a discussion on each of the following topics. When necessary, define the term, explain the term, discuss the purpose and use, and provide sample calculations. [1] Live load and its variation with tributary area [Tributary Reduction Factor] for a column in a multi-story building. [2] Design Principles for Structures, and the philosophies behind “Limit States Design”.
Write code in SAS to do each of the following I have posted the data below...
Write code in SAS to do each of the following I have posted the data below from a pace delimited data set consisting of 66 randomly selected cars Upload the data set to SAS and store it as a SAS data set called cars. Make sure the full values are stored for all character variables. Create a comparative bar chart (with appropriate title and labels) displaying the brands of each car by fuel type (so that fuel type is on...
For each of the following propositions the first word in your answer should be the word...
For each of the following propositions the first word in your answer should be the word True or the word False followed by a brief explanation as to why the proposition is true or false. assume that Frank and Athena can produce either chairs or tables. If Athena has a comparative advantage in producing chairs, then she would be able to sell chairs for a higher price than Frank.
1. For each of the following propositions construct a truth table and indicate whether it is...
1. For each of the following propositions construct a truth table and indicate whether it is a tautology (i.e., it’s always true), a contradiction (it’s never true), or a contingency (its truth depends on the truth of the variables). Also specify whether it is a logical equivalence or not. Note: There should be a column for every operator. There should be three columns to show work for a biconditional. a) (P Λ ¬Q) ⇔ ¬(P ⇒ Q) b) (¬? V¬?)...
Identify the three (3) common financial statements for a business. In your answer define each statement...
Identify the three (3) common financial statements for a business. In your answer define each statement and tell the function, need, and purpose of the statement. Answer should be 150 words or more.
Complete the following short-answer questions (3 pts each). SHORT ANSWER: An English teacher is interested in...
Complete the following short-answer questions (3 pts each). SHORT ANSWER: An English teacher is interested in whether using computer writing assignments will improve his students’ writing skills. He decides to use the computer writing assignments in one of the two freshman English classes that he teaches. Which type of quasi-experimental design do you recommend for this study? Why? Answer: SHORT ANSWER: Identify two reasons that some researchers see single-case or small-n designs as superior to designs in which many participants...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT