Question

Giving Medals.

If Amelia finishes her homework, then she will go to the park.

Which of these is logically equivalent to the given statement?

If Amelia did not go to the park, then she did not finish her homework.

If Amelia did not finish her homework, then she will go to the park.

If Amelia goes to the park, then she did not finish her homework.

If Amelia finishes her homework, then she cannot go to the park.

Answer 1

So your original statement is "If Amelia finishes her homework, then she will go to the park."

Can you identify its contrapositive?

Answer 2

Saying, your original statement is \(p \rightarrow q\)
contrapositive is \(\text{not}~q\rightarrow\text{not}~p\)

Answer 3

original statement is always logically equivalent to its contrapositive

hope this helps

Answer 4

oh so its "If Amelia did not go to the park, then she did not finish her homework" ? @geerky42

Answer 5

yep that's right