/sci/ - Science & Math

>>15664908
It is right, it is just that ors in formal logic are retarded and not consistent with day to day english. So, if you see a either in a propositional logic problem, you need to assume it is not exclusive. On top of that, their decision to have ~p be 'get to work on time' is retarded because it is represents a negation of a negative action which can cause confusion. What they should have done is have p be 'get to work on time' and q be 'you are fired'. You can see in picrel that the two statements are in fact equal, but the xor is not.
You have to think about it, not from an intuitive logical sense, but from whether a conclusion is valid given solely the supplied premises ex:
using ~p and q truth values then 'either'=XOR can't be valid as
you get to work on time: ~p = 1
you are fired: q = 1
then: ~p xor q = 0
while: p -> q = 1
as the validity of conditionals is always true if the antecedent is false as the proposition only indicates a correlation between the two values when it is true.
Rewritten in english:
The only way I can be fired is if:
I either get to work on time or I am fired, but not both
If I don't get to work on time then I am fired
This can't be true because
I got to work on time
yet I was still fired
tldr; you aren't retarded, the problem is correct, but the language of the problem is retarded