Answered

Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

Question 8 of 18

Refer to the following statement to answer parts (a) through (c) below:

You did not mow the lawn or you left the room a mess.

(a) Write the statement in symbolic form. Assign letters to simple statements that are not negated. Choose the correct answer:

A. Let [tex]p[/tex] = "you did not mow the lawn" and let [tex]q[/tex] = "you left the room a mess": [tex]\sim p \vee q[/tex]

B. Let [tex]p[/tex] = "you mowed the lawn" and let [tex]q[/tex] = "you left the room a mess": [tex]\sim p \wedge q[/tex]

C. Let [tex]p[/tex] = "you did not mow the lawn" and let [tex]q[/tex] = "you left the room a mess": [tex]\sim p \vee q[/tex]

D. Let [tex]p[/tex] = "you mowed the lawn" and let [tex]q[/tex] = "you left the room a mess": [tex]\sim p \vee q[/tex]

(b) Construct a truth table for the symbolic statement in part (a).

[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
$p$ & $q$ & $\sim p$ & $\sim p \vee q$ \\
\hline
T & T & F & T \\
\hline
T & F & F & F \\
\hline
F & T & T & T \\
\hline
F & F & T & T \\
\hline
\end{tabular}
\][/tex]

(c) Determine the truth value of the statement if you did not mow the lawn and you left the room a mess.

(Provide an explanation or choose the correct answer based on the truth table.)

Sagot :

GinnyAnswer
## a. Write the statement in symbolic form.
We are given the statement:

- "You did not mow the lawn or you left the room a mess."

Let's assign letters to the simple statements:
- Let [tex]\( p \)[/tex] be "You did not mow the lawn."
- Let [tex]\( q \)[/tex] be "You left the room a mess."

The statement to symbolize is:

- "You did not mow the lawn or you left the room a mess."

In symbolic form, this would be written as:
[tex]\[ \text{Answer: } \ p \vee q \][/tex]

### Choosing the correct answer:
A. [tex]\(\sim p \wedge q\)[/tex]: This represents "It is not the case that you did not mow the lawn AND you left the room a mess." -> Incorrect
B. [tex]\(\sim p \wedge q\)[/tex]: This represents "It is not the case that you mowed the lawn AND you left the room a mess." -> Incorrect
C. [tex]\( p \vee q \)[/tex]: This represents "You did not mow the lawn OR you left the room a mess." -> Correct
D. [tex]\(\sim p \vee q\)[/tex]: This represents "It is not the case that you mowed the lawn OR you left the room a mess." -> Incorrect

The correct answer is C.

## b. Construct a truth table for the symbolic statement in part (a).

Let's create the truth table for [tex]\( p \vee q \)[/tex]:

| [tex]\( p \)[/tex] | [tex]\( q \)[/tex] | [tex]\( p \)[/tex] | [tex]\( q \)[/tex] | [tex]\( \sim p \)[/tex] | [tex]\( \sim p \vee q \)[/tex] |
| ------ | ------ | ------ | ------ | ------ | ------ |
| T | T | F | T | F | T |
| T | F | F | F | T | F |
| F | T | T | T | F | T |
| F | F | T | F | T | T |
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.