Creating vs. containing multiple conditional statements

[JuBe]

Perhaps I'm just missing some simple indicator, but I've struggled on a few occasions to distinguish the difference between a rule that contains multiple conditional statements (such as the third rule in #2 on p. 205) and a rule that creates multiple conditional statements (such as the second rule in December 2000, Game #5 on p. 249).

Or can I always break those "and/or" statements down further?

[Dave Killoran]

Hi JuBe,

Thanks for the question. The two rules you reference are fundamentally the same. They both contain conditional statements that create a diagram with multiple sufficient conditions. Diagrams with multiple sufficient conditions can, depending on the circumstances, then be used to create multiple single diagrams (which is a topic that, coincidentally, I'm currently writing about for the new edition of the Logic Games Bible that comes out early in 2013, so this is timely ).

Let's use the example from page 205:

The rule reads: "If Operations or Sales is offered, then Accounting is also offered."

Operations = O
Sales = S
Accounting = A


As a single conditional statement, there are two parts to the sufficient condition (O and S), that are joined by an "or" operator. That sufficient condition leads to a necessary condition of A:

O
or A
S

This is a fully integrated diagram that contains all of the information in the given sentence.

However, because of the "or" operator, the occurrence of either individual component of the sufficient condition (O or S) will force the necessary condition to occur. Thus, if O occurs, then A must also occur:

O A

And if S occurs, A must also occur:

S A

Thus, writing out the two statements separately is equally valid. The decision is a personal one, and it also depends on aspects of the other rules (sometimes other rules link to only part of this rule, or don't link neatly, etc).

Note that if the operator in the sufficient condition is "and," then the two statements cannot be written out separately because it is the single, joint occurrence of the two variables that forces the necessary condition to occur. So, a statement such as, "If Operations and Sales are both offered, then Accounting is also offered" would yield only a single integrated diagram. The occurrence of O alone, for example, would not meet the specifications of the sufficient condition, so a diagram with just O as the sole sufficient condition would be invalid.

So, what happens if the if the necessary condition has multiple parts instead of the sufficient? In that case, the situation is reversed, and an "or" operator does not yield the ability to create two separate diagrams whereas an "and" operator does allow for two separate diagrams.

Please let me know if that helps. Thanks!

[JuBe]

So, what happens if the if the necessary condition has multiple parts instead of the sufficient? In that case, the situation is reversed, and an "or" operator does not yield the ability to create two separate diagrams whereas an "and" operator does allow for two separate diagrams.

Please let me know if that helps. Thanks!

Thanks for answering that. So in this case if the necessary condition operates on an "and" basis, the contrapositive would allow me to break the diagram up (as it would be switched to an "or" in the sufficient condition), correct?

~Justin

[Dave Killoran]

Hi Justin,

Yes, that is correct!

If the rule reads: "If Operations is offered, then Accounting or Sales is also offered," the the diagram is solely:

A
O or
S

Because it is just at least one of the two, you can't separate it into two separate component statements.

However, if the rule reads: "If Operations is offered, then Accounting and Sales are also offered," the the single diagram is:

A
O and
S

Because O forces both of A and S to occur, the two individual sub-statements also apply:

O A

and

O S

Please let me know if that helps. Thanks!