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I can't figure out what is meant in my text books with the "Either / Or" statements. I'm in a math proof class trying to wrap my head around this. See example below.

Either Jim or Bob has red hair
P = Jim has red hair
Q = Bob has red hair

Does this mean:

P v Q

or

(P v Q) ^ (~P v ~Q)

Thanks

polyhedron
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    I understand it looks like a duplicate. I guess it's ambiguous in english, as I've seen it used both ways. – polyhedron Aug 31 '16 at 02:47
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    In formal logic, you would generally translate it to just OR, rather than XOR. So the "either" has no formal meaning. But in practice, in natural language mathematics it is ambiguous whether the "either" is meant to imply that only one case can hold. – Carl Mummert Aug 31 '16 at 02:50

1 Answers1

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There is nothing to get confused. Imagine what any person who has not studied mathematics beyond high school would understand by this statement. It is exactly that.

P Vanchinathan
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    In my experience, either P or Q is an ambiguous English sentence, sometimes meaning P or Q and sometimes meaning P xor Q. – Zev Chonoles Aug 31 '16 at 02:46
  • @ZevChonoles: True. But in introductory logic, this is the meaning and one need split hair for a simple thing while there are enough confusing things at an advanced stage – P Vanchinathan Aug 31 '16 at 02:52