1.
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)