Lesson 3 states the order for completing truth tables is: standard variables, negated variables, propositions in (). Yet I noticed while watching the Lesson 3 session on the DVD and in the example at the bottom of page 23, the operations are not always followed in that precise order; sometimes the parenthesis are completed prior to the negation. How important is this order? Does it matter only if there is a negation within the parenthesis, as in the example at the top of p 23?
Thank you for the good question. That order is one that should always work, but if a student knows what he is doing that order is not always necessary to get a correct answer. In the example on the bottom of page 23, the ~Y could have been done prior to the (A v X), but it really makes no difference. And yes, one of the things that will affect this is whether there is a negation of a proposition within the parentheses. If so, then of course one must do the negation first.
It is analogous to arithmetic. If you have (5 + 9) * -7, it matters little whether you think of doing the addition of 5 + 9 first, or considering the negative of the 7 first. But if you have (-5 + 7), then you have to think of the negative first (you could not do 5 + 7 and then make it negative).