Answered

Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Join our platform to connect with experts ready to provide accurate answers to your questions in various fields. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

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 this was helpful. Please come back whenever you need more information or answers to your queries. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.