QuestionFind the converse, inverse, and contrapositive of: "If you visit your grandparents, then you can go to the park."
Studdy Solution
STEP 1
Assumptions1. The original statement is "If you visit your grandparents, then you can go to the park."
. The converse of a statement switches the hypothesis and the conclusion.
3. The inverse of a statement negates both the hypothesis and the conclusion.
4. The contrapositive of a statement switches and negates both the hypothesis and the conclusion.
STEP 2
First, let's identify the hypothesis and the conclusion of the original statement. The hypothesis is "you visit your grandparents" and the conclusion is "you can go to the park."
STEP 3
Now, let's write the converse of the original statement. The converse switches the hypothesis and the conclusion.
STEP 4
Next, let's write the inverse of the original statement. The inverse negates both the hypothesis and the conclusion.
STEP 5
Finally, let's write the contrapositive of the original statement. The contrapositive switches and negates both the hypothesis and the conclusion.
STEP 6
Now, let's identify the correct statements from the given options. The converse statement is option D. "If you can go to the park, then you visit your grandparents."
STEP 7
The inverse statement is option C. "If you did not visit your grandparents, then you cannot go to the park."
STEP 8
The contrapositive statement is option C. "If you cannot go to the park, then you did not visit your grandparents."
The converse, inverse, and contrapositive of the statement "If you visit your grandparents, then you can go to the park" are as followsConverse "If you can go to the park, then you visit your grandparents."
Inverse "If you did not visit your grandparents, then you cannot go to the park."
Contrapositive "If you cannot go to the park, then you did not visit your grandparents."
Was this helpful?
