Answered

Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Ask your questions and receive precise answers from experienced professionals across different disciplines. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

The statement [tex]\( p \rightarrow q \)[/tex] represents "If a number is doubled, the result is even."

Which represents the inverse?

A. [tex]\( \sim p \rightarrow \sim q \)[/tex] where [tex]\( p \)[/tex] = a number is doubled and [tex]\( q \)[/tex] = the result is even

B. [tex]\( q \rightarrow p \)[/tex] where [tex]\( p \)[/tex] = a number is doubled and [tex]\( q \)[/tex] = the result is even

C. [tex]\( \sim p \rightarrow \sim q \)[/tex] where [tex]\( p \)[/tex] = the result is even and [tex]\( q \)[/tex] = a number is doubled

D. [tex]\( q \rightarrow p \)[/tex] where [tex]\( p \)[/tex] = the result is even and [tex]\( q \)[/tex] = a number is doubled

Sagot :

GinnyAnswer
To determine the inverse of the conditional statement [tex]\( p \rightarrow q \)[/tex], we need to understand the logical structure of such statements.

First, let's examine the given conditional statement:
[tex]\[ p \rightarrow q \][/tex]
where:
- [tex]\( p \)[/tex] is "a number is doubled"
- [tex]\( q \)[/tex] is "the result is even"

The inverse of the conditional statement [tex]\( p \rightarrow q \)[/tex] is [tex]\( \sim p \rightarrow \sim q \)[/tex]. This means that if [tex]\( p \)[/tex] is false, then [tex]\( q \)[/tex] should also be false.

Now, let's break it down step by step:

1. Identify [tex]\( p \)[/tex] and [tex]\( q \)[/tex]:
- [tex]\( p \)[/tex]: a number is doubled
- [tex]\( q \)[/tex]: the result is even

2. Determine the negations ([tex]\(\sim p\)[/tex] and [tex]\(\sim q\)[/tex]):
- [tex]\(\sim p\)[/tex]: a number is not doubled
- [tex]\(\sim q\)[/tex]: the result is not even

3. Form the inverse statement ([tex]\(\sim p \rightarrow \sim q\)[/tex]):
- If a number is not doubled, then the result is not even.

Given this breakdown, let's compare the provided options:

1. [tex]\(\sim p \rightarrow \sim q\)[/tex] where [tex]\( p = \)[/tex] a number is doubled and [tex]\( q = \)[/tex] the result is even:
- This correctly represents the inverse of the original statement.

2. [tex]\( q \rightarrow p\)[/tex] where [tex]\( p = \)[/tex] a number is doubled and [tex]\( q = \)[/tex] the result is even:
- This represents the converse, not the inverse.

3. [tex]\(\sim p \rightarrow \sim q\)[/tex] where [tex]\( p = \)[/tex] the result is even and [tex]\( q = \)[/tex] a number is doubled:
- This reverses the roles of [tex]\( p \)[/tex] and [tex]\( q \)[/tex] and is incorrect.

4. [tex]\( q \rightarrow p\)[/tex] where [tex]\( p = \)[/tex] the result is even and [tex]\( q = \)[/tex] a number is doubled:
- This again represents the converse but with [tex]\( p \)[/tex] and [tex]\( q \)[/tex] reversed, and is incorrect.

The correct option is:
[tex]\[ \sim p \rightarrow \sim q \text{ where } p = \text{a number is doubled and } q = \text{the result is even} \][/tex]

Thus, the inverse of the given statement is represented by the first option. The correct answer is:
[tex]\[ 1 \][/tex]
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. 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.