Question

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

Answer 1

wat do u think?

Answer 2

i dont no

Answer 3

well, all 3 mean different things, so the last option

Answer 4

try write in in symbolic form, hint: dog wags its tail is p the dog is calm is q

Answer 5

none are equivalent

Answer 6

so it's \[I.p\to\neg q\\ II. \neg q\to p \\III.q\to\neg p\]
since by modus tollens\[p\to\neg q\Rightarrow q\to \neg p \\\therefore I\text{ imply } III\] it can be said that I equals III

Answer 7

Modus Tollens: \[\frac{P\to Q,\neg Q}{\therefore \neg P}\] 1. P implies Q, and the second premise, Q , is false
2. Then it can be logically concluded that P must be false.

Answer 8

@black12 what do you think?

Answer 9

it loks good