1.3. Types of Mathematical Logic

Try these first

1. 1.

   What is a proposition? Give an example.

   Hint

   Think of a statement that can only be true or false.

2. 2.

   What does a propositional variable represent?

   Hint

   Consider what we use to represent unknown values.

3. 3.

   What does a propositional variable represent?

   • A statement that is always true
   • A variable that can take any truth value
   • An operator in logic

   Hint

   Think of what we use to denote statements in logical expressions.

4. 4.

   True or False: In propositional logic, a statement can be both true and false.

   • True
   • False

   Hint

   Reflect on the definition of a proposition.

5. 5.

   Given propositions p: 'It is raining' and q: 'The ground is wet', construct the truth table for 'p → q'. Explain each truth assignment.

   Hint

   Consider weather examples and how one leads to the other.

6. 6.

   Create distinct logical operators for p and q with truth assignments and describe their significance.

   Hint

   Follow through with the combinations from truth tables.