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LGB p.318 Group Setup Practice Drill #2

mp1224
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Hello,

For the second question of the Grouping Setup Practice Drill in Chapter 5 ("A business school offers at least one of the following seven courses..."), I was wondering how you would diagram the contrapositives for the first two rules - A :arrow: F and not E; L :arrow: E and not M.

Thank you!
Dave Killoran
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Hi MP,

Thanks for the question! Those would be:



    F
    or :arrow: A
    E



    E
    or :arrow: L
    M



Please let me know if that helps. Thanks!
Dave Killoran
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mp1224
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Hi Dave,

Thanks for the reply!

On a similar note, in the case of a conditional statement such as "If M is selected, then neither J nor O can be selected" (p. 410), instead of diagramming this rule as: M :dblline: J and M :dblline: O, would it also be correct to depict it as:

M :arrow: J and O ?

If this is also correct, what is the reasoning behind choosing to depict it the first way over the second?
Adam Tyson
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That would also be correct, mp1224, so good job there! We choose to show it with two double-not arrows because they save us the trouble of having to diagram a contrapositive, and because for many students splitting the rule into two rules this way makes it much easier to manage. No worrying about converting "and" to "or", and no mistakenly assuming that the necessary conditions have any relationship to each other. It becomes "these two cannot be selected together" and also "those two cannot be selected together" - boom, done!

That said, your diagram is correct, and you would at least want to consider the contrapositive, if not actually draw it out in your diagram. That would be:

J
or :arrow: M
O

Play around with both approaches and use whichever one you find more useful and efficient!
Adam M. Tyson
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kg70382
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On page 320, I'm not sure how the sub-inferences were derived. Can you explain the steps of how the inferences for O and E cannot be selected together, S and E cannot be selected together, If O then F, and If S then F were made?

Also, What is the procedure/logic behind linking conditional statements with two sufficient conditions, two necessary conditions, or both? For example: How would I link (If O or S then A) with (If A or B then C)? Does the presence of the "or" or "and" effect how the statements can be linked?

Thank you in advance.
Adam Tyson
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You bet, kg70382! Here are the steps for making those inferences:

First, we have the last rule: if either O or S is offered, then A must also be offered.

Then, we link that rule to the first rule: if A is offered, F is offered and E is not offered.

That gives us this chain (which should also help answer your second question):

O                         F
or :arrow: A :arrow: &
S                         E

This chain tells us that whenever O or S is selected, everything after those variables must occur. A is offered, F is offered, and E is not offered. So, we get:

O :arrow: F
S :arrow: F
O :arrow: E
S :arrow: E

All of those inferences come from the chain connecting the last rule to the first rule, and that is how you diagram those "and" and "or" chains. Draw your conditional arrows pointing right from the conjunction, with the variables stacked vertically to allow you to make additional chains more easily.

I hope that helps clarify that for you!
Adam M. Tyson
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