If X, then not Y. If not Y, then Z. Y is true so:

Question

If X, then not Y. If not Y, then Z. Y is true so:

What is X and Z

Answer 1

This is an interesting question. Contemporary formal logic systems would evaluate this as follows:

The "if X then not Y" is symbolized as X > ~Y. Y is true, so ~Y is false. With implication (>), we cannot have a false consequent (the term after the operator) and a true antecedent (the term before the operator), so X must be false. For example, consider the claim, "If Gina gets 100% on the test, then she will pass the course." If we discover that Gina did not pass the course -- the consequent is false -- then we can know that she did not get 100% on the test. The fancy word for this is "sufficient cause." Getting 100% was a sufficient cause of passing the course.

The second part, "if not Y then Z," is symbolized is ~Y > Z. Y is true, so this means the antecedent is false (because it is negated). If the antecedent is false, then the consequent can be true OR false. We don't know which.

So, altogether, X is false, and Z could be true or false.

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