Question

translating symbolic conditional statements
given
p: 3x + 7 = -5
q: 4x + 12 = -4
which is the contrapositive of p → q?
if 4x + 12 = -4, then 3x + 7 = -5.
if 3x + 7 ≠ -5, then 4x + 12 ≠ -4.
if 3x + 7 = -5, then 4x + 12 = -4.
if 4x + 12 ≠ -4, then 3x + 7 ≠ -5.

Explanation:

Step1: Recall contrapositive rule

The contrapositive of a conditional statement \(p
ightarrow q\) is \(
eg q
ightarrow
eg p\).

Step2: Identify \(

eg p\) and \(
eg q\)
Given \(p:3x + 7=- 5\) and \(q:4x + 12=-4\), then \(
eg p:3x + 7
eq - 5\) and \(
eg q:4x + 12
eq - 4\).

Step3: Form the contrapositive

The contrapositive \(
eg q
ightarrow
eg p\) is "If \(4x + 12
eq - 4\), then \(3x + 7
eq - 5\)".

Answer:

If \(4x + 12
eq - 4\), then \(3x + 7
eq - 5\)