Question

Help i need to know if these are logically equivelent
Statement conditional: If I don’t use GeoGebra to help the city, then Dr. Madness will defeat us.
Code 1 (inverse): If I use GeoGebra to help the city, then Dr. Madness won’t defeat us.
Code 2 (converse): If Dr. Madness defeats us, then I didn’t use Geogebra to help the city.
Code 3 (contrapositive): If Dr. Madness doesn’t defeat us, then I used Geogebra to help the city.

From the conditional statement that you wrote, determine if the inverse, converse, and contrapositive are logically equivalent. Explain for each statement why

Answer 1

A statement and its contrapositive are logically equivalent.
For the statement, If ~ GG, then Defeat.
The contrapositive of that is the following:
If ~ Defeat, then ~ ~ GG.
That simplifies to If there is no defeat, the GG was used.

For the answer, I would select:

Code 3 (contrapositive): If Dr. Madness doesn’t defeat us, then I used Geogebra to help the city.
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Note: The inverse and converse of a given statement are logically equivalent to each other but not to the original statement.

So, these two are logically equivalent:

Code 1 (inverse): If I use GeoGebra to help the city, then Dr. Madness won’t defeat us.
Code 2 (converse): If Dr. Madness defeats us, then I didn’t use Geogebra to help the city.

That is because the inverse is the contrapostive of the converse.

Answer 2

thanks