Determine if the following arguments are valid or invalid by

Determine if the following arguments are valid or invalid by analyzing them and identifying if Universal Modus Ponens, Universal Modus Tollens or one of the fallacies were used. Carefully define all predicates and universe of discourse you are using. Also give a counter example for the invalid arguments using a complete sentences to explain why it is invalid.

(2) All integers can be written as the ratio of an integer a and a non-zero integer b. 6 can be written as a ratio of an integer a and a non-zero integer b. Therefore 6 is an integer

Solution

INvalid argument

All integers can be written as ratio of an integer a and a non zero integer b. This statement is correct. But if a number can be written as a ratio of integer a and a non zero integer b then it need not be an integer.

Counterexample:

2/3 is not an integer and it is a ratio of integers.