The problem today was the difference between using a “vel” for “nor” vs. using a “dot” for nor, the other was where the parenthesis were when the word both was used. We (the kids too) saw a difference in a couple of them – but one looked exactly like the other – with two different symbolic statements.
Any assistance would be greatly appreciated!
There are two ways to write “neither p nor q”:
1) ~(p ∨ q)
2) ~p • ~q
As for the use of “both”, the phrase “not both p and q” should be ~(p • q), whereas “both not p and not q” should be (~p • ~q). So the proposition “Betty and Jon are not both eighth graders” could be symbolized ~(B • J), while the proposition “Betty and Jon are both not eighth graders” would be (~B • ~J).