P: A → BP: ?C: B–some–C

thomas19 December 3, 2019

Reversed, but not negate?

How can the contrapositive of the answer be considered correct, when it's only being reversed and not negated?

Replies

Create a free account to read and take part in forum discussions.

Already have an account? log in

Irina December 3, 2019

@thomas19,

We cannot use transposition with a "particular"statement, i.e. statement that includes a quantifier, such as X - some - Y. "Some" statements can only be reversed:

X - some - Y
Y - some - X

are logical equivalents.

I believe it is covered in the lecture on quantifiers.

Let me know if you have any other questions.

Raechel-Brodsky May 17, 2020

Does it necessarily help us to make the contrapositive in this particular problem? I was able to see a connection between A and C.. Is that okay?

Lamont December 31, 2021

I didn't see this answer following logically with the contrapositive. So no, as I review the diagram, the contrapositive, and the fact that Irina and the lectures stressed quantifiers, we only reverse.

Jay-Etter January 26, 2022

Hi @Lamont, just wanted to confirm for this one that yes there isn't really such a thing as a contrapositive for quantifier statements, it's just that the order doesn't matter. "Some Xs are Ys" means the same thing as "Some Ys are Xs".