How to write the negation of a biconditional? I have two statements $p$ and $q$ such that:
Statement $p$: Ravi reads Mathematics
Statement $q$: Ravi reads Chemistry
Now, I am required to write the negation of $p \iff q$, i.e., I need to write $\lnot (p \iff q)$, which, if I understand correctly, is, by definition: $(p \land \lnot  q) \lor(\lnot p \land q )$
So, according to me, it should be as follows:
Ravi reads Mathematics and not Chemistry or Ravi doesn't read Mathematics and reads Chemistry.
But, the book states the answer to be as follows:
Ravi reads neither Mathematics nor Chemistry
Are the two statements equivalent? Or am I going wrong here?

Check question 3 (e) for the question asked here

The answer for question 3 (e)
 A: You are exactly right, and your book is wrong.
Some equivalent ways to write $\lnot (p \iff q)$ are
$$
\begin{split}
\lnot (p \iff q) &\equiv \lnot(p \implies q) \lor \lnot(q \implies p) \\
&\equiv (p \land \lnot q) \lor (\lnot p \land q) \\
&\equiv p \oplus q.
\end{split}
$$
(The last expression uses the XOR ("exclusive or") operator, $\oplus$.)
However you choose to write it, it is equivalent to what you said:
"Ravi reads Mathematics and not Chemistry or Ravi doesn't read Mathematics and reads Chemistry.
"
OP, don't be discouraged by the rude or confusing answers in this thread. Trust in your logic!
A: Your reasoning is correct. You can rewrite the negation of the biconditional as $ (p \land \lnot  q) \lor(\lnot p \land q )$ which is the same as your english sentence. The sentence your book has is equivalent to $\lnot p \land \lnot q$ which is certainly not equivalent to $\lnot (p \iff q)$ since they don't have the same truth value when $p,q$ are both false.
Either your book is wrong or you have misunderstood what the problem is asking. Maybe it was asking for the negation of the disjunction, $\lnot (p \lor q)?$
Edit: Now that you've posted pictures of the book I can definitely say that the book is wrong.
