Boolean operator in Queen problem

Question

In this paper, (page 28) I see the rule for there must be a queen in each row.

My question is shouldn't it be:

 Xi1 & Xi2 &....XiN

...instead of:

 Xi1 or Xi2 or....XiN

Answer 1

The text has it correct. The $X_{i1} \lor X_{i2} \lor \dots \lor X_{iN}$ means a queen will be on row $i$ and column $1$, or it will be on row $i$ and column $2$, $\dots$ or it will be on row $i$ and column $N$ (in other words, a queen will be somewhere on row $i$). Now you want this for all rows $i$, that is where the logical and comes in. You could write it as $$(X_{11} \lor X_{12} \lor \dots \lor X_{1N})\tag{*}\\ \land (X_{21} \lor X_{22} \lor \dots \lor X_{2N})\\ \vdots\\ \land(X_{N1} \lor X_{N2} \lor \dots \lor X_{NN}), $$ or you could do it more concisely (as the authors of the text did): For all $i$: $$X_{i1} \lor X_{i2} \lor \dots \lor X_{iN},$$ which is the same as $(*)$.