Express the following statements in Propositional Logic: 1. If P is false, then we know that Q is also false. 2. Q and P are either both false or both true. 3. Either P is true or Q is true. 4. Both P and Q are true and M is false. 5. John is tall and Peter has short hair. (define the proposition symbols you use). Solution 1. If P is false, then we know that Q is also false. ¬(P¬Q)(¬PQ) 2. Q and P are either both false or both true. ¬(P¬Q)(¬PQ) 3. Either P is true or Q is true. (P¬Q)(¬PQ) 4. Both P and Q are true and M is false. (PQ)M 5. John is tall and Peter has short hair. (define the proposition symbols you use). John is tall = P Peter has short hair = Q The proportional logic statement would be (PQ) .