P=he studies medicine ,q=he gets agood job,r=he gets a good wage.p implies q,q implies r,not r ,not p check the validity of ghe argument using truth table?

To check the validity of the argument using a truth table, we need to list all possible combinations of truth values for the propositions P, Q, and R, and then evaluate the truth value of the argument for each combination.

Let's create a truth table:

| P | Q | R | P implies Q | Q implies R | not R | not P |
|---|---|---|-------------|-------------|-------|-------|
| T | T | T | T | T | F | F |
| T | T | F | T | F | T | F |
| T | F | T | F | T | F | F |
| T | F | F | F | T | T | F |
| F | T | T | T | T | F | T |
| F | T | F | T | F | T | T |
| F | F | T | T | T | F | T |
| F | F | F | T | T | T | T |

Now, let's evaluate the truth value of the argument for each row:

1. P implies Q is true (T implies T is true).
2. Q implies R is true (T implies T is true).
3. not R is false (not T is false).
4. not P is true (not T is true).

Since the argument is valid when all premises are true, and the conclusion is true, we can conclude that the argument is valid.