Question

What is the converse and inverse of the statement? If charles wrote a sonata, then snoppy did not dance a jig.

Answer 1

would the converse be if snoopy did not dance a jig, then Charles wrote a sonata?

Answer 2

Identify your 'p' and 'q' (the hypothesis/premise and conclusion).
Converse: switch positions of 'p' and 'q'
Inverse: negate both 'p' and 'q' but leave them in the original positions.

Answer 3

Yes, that is the correct converse.

Answer 4

So that means the inverse would be if charles did write a sonata, then snoppy danced a jig?

Answer 5

I mean to say if charles did not write a sonata, the snoppy danced a jig?

Answer 6

Correct.
The way I like to remember it is that "converse" sounds like "conversation." In a conversation people talk back and forth, and that reminds me to change the order of p and q.
Negative is the 'inverse' of positive, so that reminds me to negate terms for the inverse.
Just a little mnemonic; maybe it'll help you too.

Answer 7

So that correct inverse is if charles did not write a sonata, the snoppy danced a jig?

Answer 8

Are you able to see that both the converse and inverse are logically equivalent (i.e. they mean the same thing?)

Answer 9

Yes!

Answer 10

Great. That's another important thing to remember. The converse is always equivalent to the inverse just like the contrapositive is always equivalent to the original conditional.

Answer 11

Wow, thanks!