Answered

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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].

Sagot :

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

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

When we have an implication [tex]\( p \rightarrow q \)[/tex], it reads "If [tex]\( p \)[/tex], then [tex]\( q \)[/tex]." The converse of this implication is obtained by reversing the direction of the implication, i.e., "If [tex]\( q \)[/tex], then [tex]\( p \)[/tex]."

So, given the original implication:
- [tex]\( p \rightarrow q \)[/tex]: "If [tex]\(2x = 16\)[/tex], then [tex]\(3x - 4 = 20\)[/tex]"

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

Thus, the correct answer is:
"If [tex]\( 3x - 4 = 20 \)[/tex], then [tex]\( 2x = 16 \)[/tex]."
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