When its about book recommendations, "The Logic of Scientific Discovery" by Popper is the very fundamental book about how logic helps us to build scientific theories. Russel and Whitehead are fine too, but I'd recommend Popper first when you want seriously discuss logic. Popper also deals with some popular misconceptions that are often present in discussions like this, such as misunderstanding of deduction and induction, or what a scientific proof means, or confusing the logic law of identity with unchangeability.