Question: Which of the following represents ¬A if A stands for " I like reading but I hate running".
My answer was:
¬A = I hate reading but I like running.
The actual answer:
¬A = I either hate reading or I like running.
I am confused to why the "and" was changed to an "or". Did the negation change the "and" to an "or"?
The statement $A$ is the same as "I like reading and I hate running", which is the intersection or conjunction of two different statements: $B$, which is "I like reading" and $C$, which is "I hate running", therefore $A = B \land C$. Using De Morgan Laws (I don't know if you know them), $ ¬A = ¬ (B \land C) = ¬ B \lor ¬ C$, which means exactly the same as the solution you expose here.