Question

deductive reasoning lesson (geometry concepts)
if i go to school, then i take math.
i dont take math.
→i dont go to school
p→q
¬q
→¬p
law of syllogism
if i go to school, then i take math.
if i take math, then i have homework.

1. what can you conclude from the law of contrapositive p→q and ~q are true

p is true
~p is true
q is true
~q is true

Explanation:

Step1: Recall law of contrapositive

The law of contrapositive states that if \(p
ightarrow q\) is a conditional statement, then \(
eg q
ightarrow
eg p\) is also true.

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

Let \(p\) be "I go to school" and \(q\) be "I take math". We are given \(p
ightarrow q\) and \(
eg q\).

Step3: Apply law of contrapositive

Since \(p
ightarrow q\) and \(
eg q\) are true, by the law of contrapositive \(
eg p\) is true.

Answer:

\(
eg p\) is True