TITLE: Negating "Zach blocks e-mails and texts from Jennifer"
QUESTION [5 upvotes]: I am reviewing some basic propositional logic. The question that I have come across that has given some confusion is Zach blocks e-mails and texts from Jennifer where I am asked to find the negation of this proposition. Here is what they provided as an answer in the book: Zach does not block e-mails from Jennifer, or he does not block texts from Jennifer.
Why couldn't the answer simply be It is not true that Zach blocks e-mails and texts from Jennifer? Why did they have to introduce the disjunction or?

REPLY [5 votes]: $P(x, y)$: x blocks emails from y
$Q(x, y)$: x blocks texts from y
$z$: Zach 
$j$: Jennifer


$P(z, j)$: Zach blocks emails from Jennifer;
  
  $Q(z, j)$:  Zach blocks texts from Jennifer.

You essentially negated: $P(z, j) \land Q(z, j)$. 
So did the text.
The text applied "distribution of negation over conjunction" (one of DeMorgan's Laws):
Start with your translation: 

"It is not the case that $[(P(z, j)$ and $ Q(z, j)]$" $$\iff \lnot[P(z, j) \land Q(z, j)]$$ $$\iff \lnot P(z, j) \lor \lnot Q(z, j)\tag{DeMorgan's law}$$ 
which is to say: not $P(z, j)$, or, not $Q(z, j)$.

You are correct with your statement that the sentence translates to $\;\;\lnot[P(z,j) \land Q(z, j)]$; It's logically equivalent to the text's answer: $\;\lnot P(z, j) \lor \lnot Q(z, j)$.