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.
