1 10 points Express the following statements in Propositiona

1. (10 points) Express the following statements in Propositional Logic:
a. If P is false, then we know that Q is also false.
b. Q and P are either both false or both true.
c. Either P is true or Q is true.
d. Both P and Q are true and M is false.
e. 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)