ns 1 P i T TTT F T 1 F Table 1 qpq p a A p T F T F F F 1 The last column gives the truth values of the premises The first column gives the corresponding truth values of the conclusion Now the argument will only be valid if whenever both the premises are true the conclusion is true This happens in the first row but not in the third row Therefore the argument is not valid Why don t you check an argument for validity now F T T E3 Check whether the following argument is valid pqV r q p pr You have seen that a proof is a logical argument that verifies the truth of a theorem There are several ways of proving a theorem as you will see in the next section All of them are based on one or more rules of inference which are different forms of arguments We shall now present four of the most commonly used rules Law of detachment or modus ponens Consider the following argument If Kali can draw she will get a job Kali can draw Therefore she will get a job To study the form of the argument let us take p to be the proposition Kali can draw and q to be the proposition Kali will get a job Then the premises are pq and p The conclusion is q So the form of the argument is P q P q Is this argument valid To find out let s construct its truth table see Table 2 Table 2 Truth table for p q A p q i e pq Ap q I P q P q pa p T T T T F F F T F F F T F In the table look at the second column the conclusion and the fourth T F CL