Given:
[tex]\( p: 2x = 16 \)[/tex]
[tex]\( q: 3x - 4 = 20 \)[/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 :

To determine the converse of the implication [tex]\( p \rightarrow q \)[/tex], we first need to understand what the converse of an implication means.

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

The original implication statement is [tex]\( p \rightarrow q \)[/tex]:
"If [tex]\( 2x = 16 \)[/tex], then [tex]\( 3x - 4 = 20 \)[/tex]."

The converse of an implication [tex]\( p \rightarrow q \)[/tex] is [tex]\( q \rightarrow p \)[/tex]. This means that we switch the hypothesis and the conclusion of the original implication.

So, for our given statements:
- [tex]\( p \)[/tex]: [tex]\( 2x = 16 \)[/tex]
- [tex]\( q \)[/tex]: [tex]\( 3x - 4 = 20 \)[/tex]

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

Now, let's review the given options to identify the one that correctly represents [tex]\( q \rightarrow p \)[/tex]:

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].

Matching this with our identified converse statement, the correct choice is:
"If [tex]\( 3x - 4 = 20 \)[/tex], then [tex]\( 2x = 16 \)[/tex]."

Therefore, the correct answer is option 4.