odd (?) spacing for logic notation

Question

I write code:

$\sim(p\land q)\iff (\sim p\lor \sim q)$

and my output is like this:

As you can see, the \land symbol is nice in between 'p' and 'q', but the \lor symbol stick somehow to the left, to the 'p' without space. I could manually "fix" it with forcefully added space, but I don't understand why the left and right side would have different output. Why in one example it stick to letter before, in second not. Am I doing something wrong? Is there better way to fix it without adding \; in math mode?

Answer 1

\sim is set up as an infix relation so has the spacing of = which affects the spacing of adjacent binary operators, you want a \mathord (like a letter) or perhaps better \mathop (like \log) symbol as you are using this as a prefix operator.

\documentclass{article}

\begin{document}

$\sim(p\land q)\iff (\sim p\lor \sim q)$

${\sim}(p\land q)\iff ({\sim} p\lor {\sim} q)$

$\mathop{{}\sim}(p\land q)\iff (\mathop{{}\sim} p\lor \mathop{{}\sim} q)$

\end{document}