An argument is said to be valid if its conclusion can be inferred from its premises. An argument that is not valid is called an invalid argument, or a fallacy. For each of the arguments below, identify the simple propositions involved, write the premises and conclusion(s) in logical notation using the identified simple propositions, and decide whether it is valid. Justify your decision.
(a) If I am wealthy, then I am happy. I am happy, therefore, I am wealthy.
(b) If Ahmed drives his car, he is at least 18 years old. Ahmed does not drive a car. Therefore, Ahmed is not yet 18 years old.
(c) If I study, then I will not fail CS 113. If I do not play cards too often, then I will study. I failed CS 113. Therefore, I played cards too often.