This is a homework question I'm working on. I think it's right but I'm just curious if I'm supposed to state the negation of "but it is always right" differently.
Find the negation of the following proposition:
Truth is not always popular, but it is always right
which means: not(p) & q
My Answer:
It is not the case that truth is not always popular, but it is always right.
(In a more simple way)
Truth is always popular, but it is not always right.
which means: p & not(q)
not(not(p)&q)<=>(p|not(q))or better
$$\neg(\neg p \land q) \Leftrightarrow ( p \lor \neg q)$$
If that what you expressed in English is
p & not(q)then it is wrong because you have to expressp|not(q). I think you have actually expressedp¬(q), so it is wrong. As you stated in your comment, the correct negation is truth is always popular, or it is not always right.