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