**MAT 230 Module Two Homework**

**General:**

- Before beginning this homework, be sure to read the textbook sections and the material in Module Two.
- Type your solutions into this document and be sure to show all steps for arriving at your solution. Just giving a final number may not receive full credit.
- You may copy and paste mathematical symbols from the statements of the questions into your solution. This document was created using the Arial Unicode font.
- These homework problems are proprietary to SNHU COCE. They may not be posted on any non-SNHU website.
- The Institutional Release Statement in the course shell gives details about SNHU’s use of systems that compare student submissions to a database of online, SNHU, and other universities’ documents.

- State whether each of the following is a statement or is not a statement and explain why. If it is a statement, give its truth value.

- Drink more water.
*No, it is not a statement; it is a command.* - Paris is the capital city of the United States of America.
*Yes, it is a statement. It is false.* - Is it going to rain tomorrow?
*No, it is not a statement; it is a question.*

This problem is similar to Example 1 and to Exercise 1 in Section 2.1 of your SNHU MAT230 textbook.

- Consider the two propositions.

p: We can buy a book.

q: We can go to a restaurant.

Write each of the following statements in symbolic notation and as English sentences.

- The conjunction (∧) of p and q.
*We can buy a book and we can go to a restaurant.*

*(p ∧ q)*

- The disjunction (∨) of p and q.
*We can buy a book or we can go to a restaurant.*

*(p v q)*

- The negation (~) of the conjunction (∧) of p and q.
*We cannot buy a book and we cannot go to a restaurant. (~p ∧ ~q)* - The negation (~) of the disjunction (∨) of p and q.
*We cannot buy a book or we cannot go to a restaurant. (~p v ~q)*

This problem is similar to Examples 2–4 and to Exercises 5 and 10 in Section 2.1 of your SNHU MAT230 textbook.

- Write the statement “Every number is more than its reciprocal” symbolically by first defining a predicate and then using a quantifier.
*R(x) is the predicate; “more than it’s reciprocal”.*

*∀x R(x)*

This problem is similar to Example 8 and to Exercise 18 in Section 2.1 of your SNHU MAT230 textbook.

- Let P(n): n
^{2}= n + 6.

- What is P(2) as a statement?
*∀n ~P(2)* - What is P(3) as a statement?
*∃n P(3)* - What is the truth value of ∀n P(n)?
*F* - What is the truth value of ∃n P(n)?
*T*

This problem is similar to Examples 8 and 9 and to Exercises 19, 20, and 21 in Section 2.1 of your SNHU MAT230 textbook.

- Complete a truth table for (p ∧ ~q) ∨ (~p ∧ q). There are multiple ways to set up the columns of a truth table, so you may need fewer or more columns than shown.

p |
q |
p ∧ ~q |
~p ∧ q |

T |
T |
F |
F |

T |
F |
T |
F |

F |
T |
F |
T |

F |
F |
F |
F |

This problem is similar to Example 5 and to Exercises 27–30 in Section 2.1 of your SNHU MAT230 textbook.

- Use the following:

p: I will watch TV.

q: I have finished my homework.

Write each of the following statements in terms of p, q, and logical connectives.

- I will watch TV if I have finished my homework.
*p⇒q* - I will watch TV only if I have not finished my homework.
*p⇒~q* - I will watch TV is a necessary condition for I have finished my homework.
*p⇐q* - I will not watch TV is a sufficient condition for I have finished my homework.
*~p⇐q* - I will watch TV if and only if I have finished my homework.
*p⇔q*

This problem is similar to Example 1 and to Exercises 1 and 2 in Section 2.2 of your SNHU MAT230 textbook. You may want to use the symbols ⇒, ⇐, or ⇔.

- Consider the following statement: If it is Friday, then Emily will go to the museum.

- Write the contrapositive of that statement.
*If Emily will not go to the museum, then it is not Friday. (~q ⇒~p)* - Write the converse of that statement.
*If Emily will go to the museum, then it is Friday. (q⇒p)*

This problem is similar to Example 2 and to Exercises 3 and 4 in Section 2.2 of your SNHU MAT230 textbook.

- Construct a truth table for (p ∧ q) ⇒ (p ∨ q). Explain how this truth table shows whether this statement is a tautology, a contradiction (absurdity), or a contingency.

This problem is similar to Example 5 and to Exercises 10–12 in Section 2.2 of your SNHU MAT230 textbook.

P |
Q |
(p ∧ q) |
⇒ |
(p ∨ q) |

T |
T |
T |
T |
T |

T |
F |
F |
F |
T |

F |
T |
F |
F |
T |

F |
F |
F |
F |
F |

*Contingency being that the result depends solely on the truth values of each variable.*

- Write each of the arguments below symbolically and then explain whether it is valid or not.

- If it is hot outside, then I will go swimming.
*p⇒q*

__I will not go swimming.__*~q*

∴ It is not hot outside.*~p*

*Not Valid*

- If it is not hot outside or if it is raining, then I will not go swimming.
*~p v q⇒~r*

__It is not raining.__*~q*

∴ I will not go swimming.*~r*

*Not Valid*

- I will go swimming if and only if it is hot outside.
*p⇔q*

__I will not go swimming.__*~p*

∴ It is not hot outside.*~q*

*Valid*

This problem is similar to Examples 2–5 and to Exercises 1–9 in Section 2.3 of your SNHU MAT230 textbook.

- Prove or disprove that if the product of two numbers (in ℕ) is even, then at least one of them must be even.

This problem is similar to Examples 8 and 9 and to Exercises 13–18 in Section 2.3 of your SNHU MAT230 textbook.

- Prove or disprove that if the sum of two numbers (in ℕ) is even, then at least one of them must be even.

This problem is similar to Examples 8 and 9 and to Exercises 23–26 in Section 2.3 of your SNHU MAT230 textbook.

hihi

Earn back money you have spent on downloaded sample

To export a reference to this article please select a referencing stye below.

Assignment Hippo (2021) . Retrive from http://assignmenthippo.com/sample-assignment/mat-230-module-two-homework

"." Assignment Hippo ,2021, http://assignmenthippo.com/sample-assignment/mat-230-module-two-homework

Assignment Hippo (2021) . Available from: http://assignmenthippo.com/sample-assignment/mat-230-module-two-homework

[Accessed 12/06/2021].

Assignment Hippo . ''(Assignment Hippo,2021) http://assignmenthippo.com/sample-assignment/mat-230-module-two-homework accessed 12/06/2021.

Want to order fresh copy of the **Sample Template Answers? ** online or do you need the old solutions for Sample Template, contact our customer support or talk to us to get the answers of it.

Our motto is deliver assignment on Time. Our Expert writers deliver quality assignments to the students.

Get reliable and unique assignments by using our 100% plagiarism-free.

Get connected 24*7 with our Live Chat support executives to receive instant solutions for your assignment.

Get Help with all the subjects like: Programming, Accounting, Finance, Engineering, Law and Marketing.

Get premium service at a pocket-friendly rate at AssignmentHippo

- Assignment Writing Guide
- Essay Writing Guide
- Dissertation Writing Guide
- Research Paper Writing Guide

- Accounts
- Computer Science
- Economics
- Engineering

Tap to ChatGet instant assignment help