Answered

Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Join our Q&A platform to get precise answers from experts in diverse fields and enhance your understanding. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

Given the original statement "If a number is negative, the additive inverse is positive," which are true? Select three options.

A. If [tex]\( p \)[/tex] = a number is negative and [tex]\( q \)[/tex] = the additive inverse is positive, the original statement is [tex]\( p \rightarrow q \)[/tex].

B. If [tex]\( p \)[/tex] = a number is negative and [tex]\( q \)[/tex] = the additive inverse is positive, the inverse of the original statement is [tex]\( \sim p \rightarrow \sim q \)[/tex].

C. If [tex]\( p \)[/tex] = a number is negative and [tex]\( q \)[/tex] = the additive inverse is positive, the converse of the original statement is [tex]\( q \rightarrow p \)[/tex].

D. If [tex]\( q \)[/tex] = a number is negative and [tex]\( p \)[/tex] = the additive inverse is positive, the contrapositive of the original statement is [tex]\( \sim q \rightarrow \sim p \)[/tex].

E. If [tex]\( q \)[/tex] = a number is negative and [tex]\( p \)[/tex] = the additive inverse is positive, the converse of the original statement is [tex]\( q \rightarrow p \)[/tex].

Sagot :

GinnyAnswer
Let's break down the given logical statements step by step. The original statement is given as:

"If a number is negative, the additive inverse is positive." This statement can be symbolized using logic notation where:
- [tex]\( p \)[/tex] represents "a number is negative"
- [tex]\( q \)[/tex] represents "the additive inverse is positive"

Thus, the original statement symbolically is:
[tex]\[ p \rightarrow q \][/tex]

Now, let's analyze each of the given options:

1. [tex]\( p \rightarrow q \)[/tex]:
- This represents the original statement "If a number is negative, the additive inverse is positive."
- This is true.

2. [tex]\( \sim p \rightarrow \sim q \)[/tex]:
- This represents the inverse of the original statement.
- The inverse changes the condition to "If a number is not negative, the additive inverse is not positive."
- This is the correct inverse form.

3. [tex]\( \sim q \rightarrow \sim p \)[/tex]:
- This does not represent the proper converse form. The correct converse changes the order of [tex]\( p \)[/tex] and [tex]\( q \)[/tex] without negation applied directly.
- So, this is not the converse.

4. [tex]\( q \rightarrow p \)[/tex]:
- This represents the converse of the original statement.
- The converse reverses the implications: "If the additive inverse is positive, then the number is negative."
- This is true as a logical converse.

Thus, analyzing each option, we can confirm:

1. [tex]\( p \rightarrow q \)[/tex] (original statement)
2. [tex]\( \sim p \rightarrow \sim q \)[/tex] (inverse)
3. [tex]\( q \rightarrow p \)[/tex] (converse)

Therefore, the selections (1, 2, 3) align correctly with the provided logical breakdown:
- Selection 1: [tex]\( p \rightarrow q \)[/tex]
- Selection 2: [tex]\( \sim p \rightarrow \sim q \)[/tex]
- Selection 3: [tex]\( q \rightarrow p \)[/tex]

Thus, the three true options are:

- [tex]\( p \rightarrow q \)[/tex] (Option 1)
- [tex]\( \sim p \rightarrow \sim q \)[/tex] (Option 2)
- [tex]\( q \rightarrow p \)[/tex] (Option 5)
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.