Hey all,

I'm trying to prove whether or not round is a shape.

I have:

StatementA: round is a shape

ConverseA: A shape is round

InverseA: If it is not round, then it is not a shape

ContrapositiveA: If it is not a shape, then it is not round

OR:

StatementB: round is not a shape

ConverseB: A Shape is not round

InverseB: If it is not a shape, then it is not round

ContrapositiveB: If it is a shape, then it is not round.

I either need to show: A) round is a shape, can show ContrapositiveA is true, or ContrapositiveB is false

B) round is not a shape, can show ContrapositiveB is true, ContrapositiveA is false.

However, I am not sure if I've formed either contrapositive correctly, since they refer to objects as being round or shapes, and not to roundness itself as being a shape (do you see what I mean?). If that is incorrect, what would be the proper contrapositives? I could also use a proof by contradiction, so maybe my contrapostive approach isn't the best.

Any thoughts?

Thanks!