Setup and Rule Diagrams

[Administrator]

Setup and Rule Diagram Explanation

This setup is still in progress. Please post any questions below!

[cmd036@bucknell.edu]

Hello Powerscore,

I had trouble nailing down the contrapositive for the final rule regarding what happens when the Tragedy is not purchased. My initial set up for the conditional statement was (no T --> M & R) to indicate that if T is not purchased then M & R will be. When coming up with the contrapositive, I reversed, negated and flipped "and" to "or" which left with with (no M, or no R, or neither -> T is purchased).

My first concern is whether or not I am right in putting "or neither" in the sufficient side of the contrapositive. Secondly, I am curious if the contrapositive as a whole is correct and would therefore restrict the possibility of all three (M, R and T) being purchased or some combination of (T&R) or (T&M) being purchased. Perhaps I am overthinking this entirely, but for some reason this felt incorrect. Any clarification is greatly appreciated. Thanks.

[Chandler H]

Hi CMD,

Your initial setup was correct—basically, if T is "out," then both M and R are "in."

T M & R

However, you'll notice that this doesn't tell us anything about what happens if T is "in." If you read the rule again, you'll see that it's entirely possible that T, M, and R are all "in" at the same time—they just can't be "out" at the same time.

Therefore, the contrapositive is a bit more difficult, but you have the right idea: If either M or R are "out," then T must be "in." This rule also includes the scenario in which neither M nor R are purchased. You could think of that like this:

M or R T

I hope that's helpful!