negation of following example (for a logical reasoning q)

[nealaguo]

Hi, just wondering how you would negate the following answer choice?

"As long as secondary students are taught with methods appropriate to their learning styles, they will devote significant effort to their studies".

I thought the negation would be: "if secondary students are taught with methods appropriate to their learning styles, they won't devote significant effort to their studies", but I don't think I am correct. Why am I wrong?


Thanks

[Rachael Wilkenfeld]

Hi nealaguo,

You did a good job on this at recognizing that it was a conditional statement---way to go!

Conditionals are not intuitive when thinking about logical opposition. The natural response would be to think of the contrapositive--that's negation of sorts. But since the contrapositive of a statement is logically equivalent to the original conditional, that can't be correct.

So how do you negate a conditional? You want something that says that the sufficient can occur without the necessary. That's the logical opposite.

Here our conditional statement can be diagrammed as

devote significant effort secondary students taught with appropriate methods.

To find the logical opposite, we'd say that students will devote significant effort to their studies EVEN IF they are not taught with appropriate methods.

The "even if" phrase is not necessarily conditional, so we don't diagram it. It's the concept that's important to understand for the negation.

The PowerScore blog has a great entry on the topic of negating conditionals here if you are interested in reading more.

Hope that helps!
Rachael

[nealaguo]

This was very helpful for me. Thanks heaps Rachael!