Or Both, not Both

arabprodigy30

If Jays, Martins, or both are in the forest then so are Harriers.


If J--> H
If M -> H , according to JY we should split when "or" is in the sufficient .


So what would the contro-positive be?


If not H-> not J?
If not H -> not M?


or would it be If not H -> not J and M ??

or is it if not H -> not J or M ?


Another question ....

But not both , or

Alan or Chris goes to park, but not both


If not A <-> C
If not C <-> A


so for not both, do we always just pick one throw it on either side of arrow and negate it?

alexroark5

for the first one you should have:

J
(two arrows, one from J, one from M) that both point to H
M

for the second,

this is correct, it is a biconditional. however be careful, "or but not both" is NOT the same as "not both"

emli1000

but not both = bi-conditional always apart

emli1000

Or in the sufficient - split
And in the sufficient- don't split

And in the necessary-split
Or in the necessary-don't split

These rules are for the in/out games

arabprodigy30

@emli1000 , oh okay makes sense ! thank you both for responding

arabprodigy30

@emli1000

Or in the sufficient - split
And in the sufficient- don't split

And in the necessary-split
Or in the necessary-don't split so this does not apply to any other games except in /out games ?


"But not both" , and " not both" @alexroark5 mentioned they are not same. Can you please help me understand how they are not same ?


ex:

You will eat apples or oranges but not both

A <-> not O (double arrow)

You will eat apples or oranges , not both


A-> not O
O->not A


How are they different ?