Conditional reasoning

[tonyk8260411]

Hi instructor

Please could you help me with this question regarding conditional reasoning. This has to do with grouping questions as well.

Conditional statement: If David is in group A, then Eric is in group B.

I understand that the diagram is D(a) ------> E(b)

But for this type of statements I don't know what is the contra positive. Could you please draw the diagram for the contra positive of this statement? I might be over thinking it a little but for in my mind I don't think the contrabpositive for this statement is a simply negation I.e. Not D(a) ------> not E(b). Or maybe it is just that simple but I am overthinking it?

Further, is there a difference if the grouping consists of two groups I.e. Group A and B only or if the group consists of three groups I.e. Group A, B and C?

Thanks v much

Tony

[James Finch]

Hi Tony,

Good questions! I'll start with the second one, as it affects the answer to the first: if we have only two groups, and know that
DA EB then we know its contrapositive will be EA DB. This logically means that the only way the two variables can be in a group together is if they are in Group B together.

Now if there are more than two possible groups, then we have to use a slightly different notation: DA EB still works, but the contrapositive becomes EB DA (that's a strikethrough if it's not readable). Because there are now multiple possible groups that the other variable can go into, not just one, so we can't draw an inference about which group the variable will fit into. However, we still know that the two variables can't be in Group A together.

Hope this clears things up!

[tonyk8260411]

Hi James

Thanks for the response.

However I still don't quite understand how does the second one work. If there are more than 2 groups then we don't have to diagram the original conditional statement? Which is D(a) -----> E(b)?

Is it the case that if in such a situation we shouldn't diagram it using conditional diagram at all?

Further, for the first question where there are only two groups. So it's simply this,
D(a) ----> E(b)
Contra positive being E(a) -----> D (b)
Can there be a situation where both E and D ends up in group (b)? I understand there can be right ?

[James Finch]

Hi Tony,

I'm sorry, when I was answering your second question I had a created a different conditional from the example you had given. My apologies; I've edited the post above to make sense of the different way one would note a conditional relationship in a two-group game versus a more-than-two-group game.

In both types, the only possibility that is excluded from happening by the rule you gave is both variables appearing in group A. Both could appear in group B together (or any other groups besides A), or in different groups, but cannot appear in A together.

Let me know if this clarifies things.