Negation in the Unless Equation

[cmorris32]

Hello!

I have a question about the instruction to negate the sufficient condition in the unless equation for conditional reasoning. I am getting confused if the sufficient condition includes the word "not."

For example: He will not get an A+ unless he studies.

Step 1 of the unless equation would be to use "study" as the necessary condition. Step 2 would be to negate the remaining condition and use it as the sufficient condition. However, when I am negating "he will not get an A+," would it just turn out to "A+" rather than "A+ (NOT)"?

So the equation would be: study --> A+?

I just want to clarify that when I am negating a condition that includes "not," it turns out to be positive because of the two negatives?

(I'm so sorry if this question doesn't make sense I didn't really know how to phrase what I am trying to say!) Thank you for your help!

[Luke Haqq]

Hi cmorris32!

From your explanation, it appears like you worked through and described everything correctly, except it appears that your final diagram ("So the equation would be: study --> A+?") flips around the necessary and sufficient conditions.

A "necessary" condition will be on the right side of the arrow:

Sufficient Necessary

You rightly describe that "Step 1 of the unless equation would be to use 'study' as the necessary condition." However, your diagram instead placed it in the sufficient position. Additionally, you worked through the A+ language correctly (by recognizing the need to negate a statement that is phrased in the negative) and rightly described it as the sufficient condition, but then instead placed it as the necessary condition.

So again, you worked through the steps correctly. "Step 1 of the unless equation would be to use 'study' as the necessary condition." Thus Step 1 would give us:

?? Study

Second, "Step 2 would be to negate the remaining condition and use it as the sufficient condition," with the negation of "he will not get an A+," simply being "A+." Putting this in as the sufficient condition, we then have:

A+ Study

In other words, "If Student got an A+, then Student studied" (which is equivalent to saying "Student will not get an A+ unless Student studies").

Hope that helps!