1. Introduction to Mathematical Logic

Try these first

1. 1.

   What is a proposition?

   Hint

   Think of a simple statement you can verify.

2. 2.

   Give an example of a logical operator.

   Hint

   What operator flips a proposition's truth value?

3. 3.

   What does a proposition represent?

   • A declarative statement that is always true
   • A statement that can be true or false
   • A mathematical operation

   Hint

   Think about its definition.

4. 4.

   The conjunction operator is true when:

   • Both propositions are false
   • At least one proposition is true
   • Both propositions are true

   Hint

   Consider how AND functions.

5. 5.

   Create a truth table for the expression (p ˄ q) V r. How does the truth of this statement change based on the values of p, q, and r?

   Hint

   Remember that V represents OR and ˄ represents AND.

6. 6.

   Given a logical statement P: 'If I study, then I will pass' and the statement Q: 'I did not pass', determine the validity of the implication P → Q.

   Hint

   Think through the conditions of the implication carefully.