QuestionWrite the converse, inverse, and contrapositive of the statement below.
If the band does not play rock music, then the band does not have a guitarist.
Choose the correct converse.
A. The band plays rock music or the band does not have a guitarist.
B. If the band plays rock music, then the band has a guitarist.
C. If the band has a guitarist, then the band plays rock music.
D. If the band does not have a guitarist, then the band does not play rock music.
Studdy Solution
STEP 1
What is this asking?
We're taking a sentence and twisting it around in a few different ways, then picking which twisted version is the right "converse".
Watch out!
It's easy to mix up converse, inverse, and contrapositive!
Make sure you're switching the right parts of the sentence around.
STEP 2
1. Original Statement
2. Converse
3. Inverse
4. Contrapositive
5. Choose the Correct Converse
STEP 3
Let's **clearly state** our original sentence: If the band does not play rock music, then the band does not have a guitarist.
STEP 4
To find the **converse**, we **switch** the hypothesis and conclusion of the original statement.
So, our converse is: If the band does not have a guitarist, then the band does not play rock music.
STEP 5
Now, for the **inverse**, we **negate** both the hypothesis and conclusion of the original statement.
This gives us: If the band *does* play rock music, then the band *does* have a guitarist.
STEP 6
Finally, the **contrapositive**!
We're going to **negate** *and* **switch** the hypothesis and conclusion of the original statement.
It's like doing the converse of the inverse (or the inverse of the converse!). So, the contrapositive is: If the band *does* have a guitarist, then the band *does* play rock music.
STEP 7
Let's look back at our **converse**: If the band does not have a guitarist, then the band does not play rock music.
STEP 8
Now, which option matches our converse?
Option D: If the band does not have a guitarist, then the band does not play rock music. **Boom!** That's a match!
STEP 9
The correct answer is D.
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