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. Write your comments directly on this sheet. Also give a counter example for the invalid arguments using a complete sentences to explain why it is invalid.

Solution

The statement says all integers can be written as the ratio of an integer a and a nonzero integer b. Given 6 can be writtena s a ratio of an integer a and a nonzero integer b, hence 6 is an integer. This is an example of the converse of the given statement.

The converse of this statement may not be true, for example

1/2 is a ratio of the integer 1 and the non zero integer 2, but it is clearly not an integer.

Thus the fact that  6 can be writtena s a ratio of an integer a and a nonzero integer b, hence 6 is an integer cannot be justified true. This is true for a particular integer 6 , but may not be true forvall integers in general.