P 1 Premise P 2 Premise P 3 Premise . . . . . . . . . . C is a tautology. In other words, validity means that if all the premises are true, then the conclusion must be true. 3,4 Rule C 6. Answer Quite correct.
Truth tables can get awfully large.
It gets worse quickly, since each extra variable doubles the number of rows. The proof , on the other hand, is easy and requires only three lines in addition to the premises. By the end of this chapter, you should be able to look at an argument in words or symbols and decide, using your understanding of the rules of inference, whether or not it is valid. Thinking in terms of truth tables is no help towards this goal. While truth tables suffice to check the validity of statements in the propositional calculus, they do not work for the predicate calculus, and hence they do not work for real mathematical arguments.