Let $S$ represent the English statement "Sales will go up."And let $E$ represent the English statement "Expenses will go up." Now my problem is that I have trouble telling the difference between these two statements: $\neg(S\land Q)$ and $\neg S \land \neg E$. When these two statements are translated into English they sound,to me, the same. However, when you look at their truth tables they are different.
Here is my best translation of these two statements:
1) $\neg(S\land E)$ represented in English, "Both sales and expenses will not go up."(Correct me if I translated it wrong)
2)$\neg S \land \neg E$ represented in English, "Expenses will not go up and sales will not go up."(Again, correct me if I'm wrong)
I still do not understand the difference between these two statements in the English representation. They both sound the same thing to me.
Once more, I have the same trouble I have with understanding with the or-connective( $\lor$ ). Again let E and S be the same statements as before.Tell me if I might have translated them wrong.
1) $\neg (S \lor E)$ represented in English is "Neither sales nor expenses will go up."
2)$\neg S \lor \neg E$ represented in English is "Sales will not go up, or Expenses will not go up."
Yet I still have trouble understanding the difference between the English translation.
In short, can you give me some alternative example that better explains the difference, something intuitive that gives me a clear picture of the difference of the meaning between the statements I showed with the connective-or and connective-and. Thank you.