Question

I have a question about logically equivalent statements.... Which of the following statements are logically equivalent to this original statement?
Original: if the geo squad uses the geomobile and it's weapons, then, dr madness will be defeated.

Inverse: if the geosquad doesn't use the geomobile, then dr madness won't be defeated.
Converse: if dr madness is defeated, then the geosquad used the geo mobile and it's weapons.
Contra positive: if dr madness is not defeated, then the geo squad didn't use the geomobile and it's weapons.

All of them seem logically equivalent! I'm so confused

Answer 1

Unfortunately, everyone knows Dr. Madness can defeat the Geo-Squad, Geomobile or not.

Serious answer. The contra-positive is always the logical equivalent of a proposition. If it rains, then the grass outside is wet? If the grass isn't wet, then it hasn't rained. QED. You cannot say, however, that if the grass is wet, then it has rained; after all, you may very well have a sprinkler. Or that if it hasn't rained, the grass can't be wet; as we've established, there are a lot of grass-wetting forces in this world.

Answer 2

So the nosy equivalent statement is the contra positive?

Answer 3

Sorry, only