Question

translating symbolic conditional statements given p: 3x + 7 = - 6 q: 4x + 12 = - 4 which is the contrapositive of p → q? if 4x + 12 = - 4, then 3x + 7 = - 6. if 3x + 7 ≠ - 6, then 4x + 12 ≠ - 4. if 3x + 7 = - 6, then 4x + 12 = - 4. if 4x + 12 ≠ - 4, then 3x + 7 ≠ - 6.

Explanation:

Step1: Recall contrapositive rule

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

Step2: Identify \(p\) and \(q\)

Here \(p:3x + 7=- 5\) and \(q:4x + 12=-4\). So \(
eg p:3x + 7
eq - 5\) and \(
eg q:4x + 12
eq - 4\).

Step3: Form the contrapositive

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

Answer:

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