Question

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 dog wags its tail, then the dog is not calm.
II) Either the dog does not wag its tail or the dog is not calm.
III) If the dog is not calm, then the dog wags its tail.
a.I, II, and III are equivalent
b. I and II are equivalent
c. II and III are equivalent
d. I and III are equivalent
e. None are equivalent

Answer 1

e, if you make a truth table, you will see that none of them are equivalent

Answer 2

Can you please do it?

Answer 3

You sure it's not this Statement I is if p -> ~q
Statement II is ~p v ~q
Statement III is if ~q -> p

Look at statements I and II.

Either the dog wags its tail or not. If the dog does wag its tail, it is not calm. Therefore either the dog does not wag its tail or it is not calm.

Either p or ~p, and if p -> ~q can be translated as ~p v ~q.

On the other hand, what if the dog has multiple behaviors to indicate that it is not calm. Maybe it wags its tail to indicate happiness, but it also hides it tail and whimpers when frightened, another not-calm situation. Therefore, just because the dog is not calm does not mean it is wagging its tail. So III is different from I and II.

the answer is b.

Answer 4

yeah, it is b, misread it cuz I was doing it quickly in my head