Determine which, if any, of the three statements are equivalent ...

1. Determine which, if any, of the three statements are equivalent.
I) If the dog wags its tail, then the dog is not calm.
II) If the dog is not calm, then the dog wags its tail.
III) If the dog is calm, then the dog does not wag its tail.
 

I, II, and III are equivalent
I and II are equivalent
II and III are equivalent
I and III are equivalent
None are equivalent 

 2. Write the argument below in symbols to determine whether it is valid or invalid. State a reason for your conclusion. Specify the p and q you used.
 

Either the gazebo is made of wood or the vine is growing on the gazebo.
The gazebo is not made of wood.
The vine is growing on the gazebo 

3. Determine which, if any, of the three statements are equivalent. Give a reason for your conclusion. Show complete work and submit your solution to the Dropbox.
 

I) If the garden needs watering, then the garden does not need weeding.
II) Either the garden needs watering or the garden does not need weeding.
III) If the garden does not need watering, then the garden does not need weeding.

a. None are equivalent
b. I, II, and III are equivalent
c. I and II are equivalent
d. I and III are equivalent
e. II and III are equivalent