Double-Not arrow, Positive SUFF and Negative NECC, is it the

[Mi Kal]

Hi.

Double Arrow v Double Not Arrow

Is it safe to say that the Double Not Arrow is just the Contrapositive of the Double Arrow and that the Double Arrow is just the Contrapositive of the Double Not Arrow? Or does it not work that way?

An example from the LR Bible discusses "if and only if" taxes are raised then the government will have a deficit.
The answer given is:
TR GD and the Contrapositive given is -GD -TR
is that answer the same as
GD TR
or are they different? If they are different, why are they different?

Also, with "either/or," I am having difficulty seeing the construction. For example, "Either Jones or Kim will win the election. The answer in the book is
-JW KW and then
-KW JW.
I put WE J or K
and then as the Contrapositive -J and -K -WE
And I can't see why it can't be diagrammed the way I did it as opposed to the answer in the book.

Additionally, with the feast or famine example, can the diagram be
Fe Fa
since they are mutually exclusive or does it have to be the way it is answered in the book
-Fe Fa and -Fa Fe along with Fe -Fa and Fa -Fe?

Thanks.

Michael

[Luke Haqq]

Hi Michael!

Happy to try to answer your questions--

Is it safe to say that the Double Not Arrow is just the Contrapositive of the Double Arrow and that the Double Arrow is just the Contrapositive of the Double Not Arrow? Or does it not work that way?

I wouldn't think of it that way. Rather, think of a double (not) arrow as a shorthand, useful way of representing two conditional statements.

Thus A B represents

A B, and
B A

Further, A B represents

A ~B, and
B ~A

As you can see, the underlying statements that a double arrow and double not-arrow represent are not contrapositives of one another.

TR GD and the Contrapositive given is -GD -TR
is that answer the same as
GD TR
or are they different? If they are different, why are they different?

The double not-arrow statement is different from the initial statements.

TR GD -- if you have TR, then you have GD and vice versa
-GD -TR -- if you don't have GD, then you don't have TR and vice versa
GD TR -- GD and TR can never be together; if you have one, then you don't have the other

In other words, the last statement is unpacked as GD ~TR, and TR ~GD. These are different from the initial conditional statements.

-JW KW and then
-KW JW.
I put WE J or K
and then as the Contrapositive -J and -K -WE
And I can't see why it can't be diagrammed the way I did it as opposed to the answer in the book.

I think your diagram and the ones in the book are saying roughly the same thing. However, the difference between your diagram and the ones in the book is that the book indicates that the election will decidedly have a victor, and it will either be K or J. In other words, using the contrapositive from your answer, it appears like you're saying that if J or K does not win the election, then there is no winner to the election. That's slightly different from saying that "Either Jones or Kim will win the election."

To your last question, I'm unfortunately not sure which specific question in the book is being referenced--hopefully the clarifications provided above can help you tackle it!

[Mi Kal]

Thanks Luke

[jisuuu]

Hi! I said
Jones -> negated Kim
Kim -> negated Jones

Is this wrong? If so, how is it different from the correct answer
negated JW -> KW
negated KW -> JW?

In other words, why do you negate the sufficient condition first?

[Dave Killoran]

Hi! I said
Jones -> negated Kim
Kim -> negated Jones

Is this wrong? If so, how is it different from the correct answer
negated JW -> KW
negated KW -> JW?

In other words, why do you negate the sufficient condition first?

Hi J,

Yes, it is wrong. The essence of either/or is that at least one must always occur. which means if one is removed, the other has to occur. That means if you negate one (take it away(, the other occurs. That's the following:

negated JW -> KW
negated KW -> JW?


On the other hand, you diagram says that if one occurs, then the other doesn't, but in a simple either/or statement, both could occur so your statement is false.

Search this form for more either/or discussions--there are many!!

Thanks!