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Given:
[tex]\[
\begin{array}{l}
p: 2x = 16 \\
q: 3x - 4 = 20
\end{array}
\][/tex]

Which is the converse of [tex]\( p \rightarrow q \)[/tex]?

A. If [tex]\( 2x \neq 16 \)[/tex], then [tex]\( 3x - 4 \neq 20 \)[/tex].
B. If [tex]\( 3x - 4 \neq 20 \)[/tex], then [tex]\( 2x \neq 16 \)[/tex].
C. If [tex]\( 2x = 16 \)[/tex], then [tex]\( 3x - 4 = 20 \)[/tex].
D. If [tex]\( 3x - 4 = 20 \)[/tex], then [tex]\( 2x = 16 \)[/tex].



Answer :

GinnyAnswer
To find the converse of the statement [tex]\( p \rightarrow q \)[/tex], let's first understand what the original statement [tex]\( p \rightarrow q \)[/tex] means:

- [tex]\( p \)[/tex]: [tex]\( 2x = 16 \)[/tex]
- [tex]\( q \)[/tex]: [tex]\( 3x - 4 = 20 \)[/tex]
- [tex]\( p \rightarrow q \)[/tex]: If [tex]\( 2x = 16 \)[/tex], then [tex]\( 3x - 4 = 20 \)[/tex].

The converse of [tex]\( p \rightarrow q \)[/tex] is [tex]\( q \rightarrow p \)[/tex]. This means that if [tex]\( q \)[/tex] is true, then [tex]\( p \)[/tex] must also be true.

Let's now rewrite this in logical statements:

- [tex]\( q \rightarrow p \)[/tex]: If [tex]\( 3x - 4 = 20 \)[/tex], then [tex]\( 2x = 16 \)[/tex].

We can thus match this with the given answer choices:

1. If [tex]\( 2x \neq 16 \)[/tex], then [tex]\( 3x - 4 \neq 20 \)[/tex].
2. If [tex]\( 3x - 4 \neq 20 \)[/tex], then [tex]\( 2x \neq 16 \)[/tex].
3. If [tex]\( 2x = 16 \)[/tex], then [tex]\( 3x - 4 = 20 \)[/tex].
4. If [tex]\( 3x - 4 = 20 \)[/tex], then [tex]\( 2x = 16 \)[/tex].

The correct converse of [tex]\( p \rightarrow q \)[/tex] is represented by:

If [tex]\( 3x - 4 = 20 \)[/tex], then [tex]\( 2x = 16 \)[/tex].

So, choice (4) is the correct answer.

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