Answered

Solve your doubts and expand your knowledge with IDNLearn.com's extensive Q&A database. Get the information you need from our experts, who provide reliable and detailed answers to all your questions.

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 :

GinnyAnsweridn
To solve this problem, let's break down the logical implications and their inverses.

Given:
- [tex]\( p \)[/tex]: A number is doubled.
- [tex]\( q \)[/tex]: The result is even.
- The original statement is [tex]\( p \rightarrow q \)[/tex], which reads "If a number is doubled, the result is even."

The inverse of a logical implication [tex]\( p \rightarrow q \)[/tex] is [tex]\( \sim q \rightarrow \sim p \)[/tex].

We want to identify the inverse in the context of this specific problem. Let's look at each of the available answer choices in detail:

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 translates to: "If a number is not doubled, the result is not even."
- This description does not accurately capture the meaning of the inverse of the original statement [tex]\( p \rightarrow q \)[/tex], because it does not follow the correct form [tex]\( \sim q \rightarrow \sim p \)[/tex].

2. [tex]\( q \rightarrow p \)[/tex] where [tex]\( p \)[/tex] = a number is doubled and [tex]\( q \)[/tex] = the result is even.
- This translates to: "If the result is even, then the number is doubled."
- This also does not correspond to the inverse of the original statement [tex]\( p \rightarrow q \)[/tex].

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 translates to: "If the result is not even, the number is not doubled."
- This option switches the definitions of [tex]\( p \)[/tex] and [tex]\( q \)[/tex], which 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 translates to: "If the result is even, a number is doubled."
- This follows the correct form of the inverse: [tex]\( \sim q \rightarrow \sim p \)[/tex] when correctly interpreted in the context of the problem statement.

Therefore, the correct representation of the inverse is:
[tex]\[ q \rightarrow p \text{ where } p = \text{the result is even and } q = \text{a number is doubled}. \][/tex]

The correct answer is:
[tex]\[ q \rightarrow p \text{ where } p = \text{the result is even and } q = \text{a number is doubled}.\][/tex]
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Your search for solutions ends at IDNLearn.com. Thank you for visiting, and we look forward to helping you again.