Answered

IDNLearn.com offers a comprehensive solution for all your question and answer needs. Find in-depth and trustworthy answers to all your questions from our experienced community members.

If an original conditional statement is represented by [tex]\( p \rightarrow q \)[/tex], which represents the contrapositive?

A. [tex]\( q \rightarrow p \)[/tex]
B. [tex]\( \sim q \rightarrow \sim p \)[/tex]
C. [tex]\( p \rightarrow q \)[/tex]
D. [tex]\( \sim p \rightarrow \sim q \)[/tex]

Sagot :

GinnyAnsweridn
To identify the contrapositive of a conditional statement, let's start by understanding the given conditional statement [tex]\( p \rightarrow q \)[/tex]. This means "if [tex]\( p \)[/tex], then [tex]\( q \)[/tex]".

A contrapositive reverses and negates both the hypothesis and the conclusion of the original statement. Here are the breakdowns of the options provided:

1. [tex]\( q \rightarrow p \)[/tex]: This is the converse of [tex]\( p \rightarrow q \)[/tex].
2. [tex]\( \sim q \rightarrow \sim p \)[/tex]: This is obtained by negating both the hypothesis and the conclusion of the original statement and then reversing them. Thus, "if not [tex]\( q \)[/tex], then not [tex]\( p \)[/tex]".
3. [tex]\( p \rightarrow q \)[/tex]: This is simply the original conditional statement.
4. [tex]\( \sim p \rightarrow \sim q \)[/tex]: This is the inverse of [tex]\( p \rightarrow q \)[/tex].

Therefore, the contrapositive of [tex]\( p \rightarrow q \)[/tex] is [tex]\( \sim q \rightarrow \sim p \)[/tex]. The correct answer is:

[tex]\[ \sim q \rightarrow \sim p \][/tex]
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. Thank you for choosing IDNLearn.com. We’re here to provide reliable answers, so please visit us again for more solutions.