Symbolizing “nor” and “both”

Hi Jim,

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).


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