1. Prove the following using Truth Table 5 points p implies q; therefore not q implies not p

2. Verify the concluding statement using the given rules and facts. Apply the rules of inferences to prove. 15 points

Rules: Hospital can share a patient's information only if the patient provides consent. Properly authorized representative provides consent if and only if a patient provides consent. A representative is properly authorized only if the authorization is notarized.

Fact: A representative provides consent to release a patients data. The authorization of the representative was not notarized. Verify (if True or False): Hospital can share the patients data. Hint: Convert "only if" expressions into equivalent "if" statement.