1) If p is true and q is true, then p • q is true.
2) If p is true and q is false, then p • q is false.
3) If p is false and q is true, then p • q is false.
4) If p is false and q is false, then p • q is false.
Now, given the rule in conjunction, how do we determine the truth-value of the conjunctive statement p • ~q?
Let us suppose that the truth-value of p is true and q is false. So, if p is true and q false, then the statement p • ~q is true. To illustrate:
The illustration above says that p is true and q is false. Now, before we apply the rule in conjunction in the statement p • ~q, we need to simplify ~q first because the truth-value “false” is assigned to q and not to ~q. If we recall our discussion on the rule in negation, we learned that the negation of false is true. So, if q is false, then ~q is true. Thus, at the end of it all, p • ~q is true if p is true and q is false.
