Let A mean "Equation A has a solution" and B mean "Equation B has no solution." I am a little confused, so I wrote down some possibilities and I wish to see if my interpretation of the following is correct:
- Equations A and B both have no solutions. In symbols: ~A /\ ~B.
- Neither equation A nor B has a solution. In symbols: ~(A \/ B).
- Both equations A and B have no solutions. In symbols: ~(A \/ B).
If I'm correct, I want to know intuitively the difference between (1) and (3). Thanks.