Question

Are my answers for the conditional statement correct? I would just like to check them and if they're incorrect, could you let me know how to fix them? Thank you.
Statement: If I brush my teeth twice a day, then I will not get cavities.


Inverse: If I don't brush my teeth twice a day, then I will get cavities.
Truth Value: True

Converse: If I don't get cavities, then I am brushing my teeth twice a day.
Truth Value: True


Contrapositive: If I get cavities, then I am not brushing my teeth twice a day.
Truth Value: True

Answer 1

Statement: If p, then q

Inverse: If q, then p

Converse: If not p, then not q

Contrapositive: If not q, then not p.

We can see from the statement that p = brush teeth twice a day and q = not get cavities.

Thus:

Inverse: If I don't get cavities, then I brush my teeth twice a day. FALSE (for example, I might floss extra well instead. Brushing my teeth twice a day is not the only way to avoid cavities)

Converse: If I don't brush my teeth twice a day, then I get cavities. FALSE (for example, I might not eat a lot of sugar and thus I don't get cavities)

Contrapositive: If I get cavities, then I did not brush my teeth twice a day. TRUE

If this confuses you, try the example of p = cat and q = four legs. (i.e. the statement is If this is a cat, it has four legs). Try making the inverse, converse, and contrapositive, and see the truth of those statements.