1.4.3. Compound Propositions

Try these first

1. 1.

   What is a proposition?

   Hint

   Think about statements that declare something.

2. 2.

   What does the negation of a true proposition yield?

   Hint

   Negation flips the truth value.

3. 3.

   A proposition must be what?

   • Always true
   • Always false
   • Either true or false

   Hint

   Recall the definition of a proposition you learned.

4. 4.

   If p is true, then ¬p is?

   • True
   • False

   Hint

   Think about the concept of negation.

5. 5.

   Given p: 'It is raining' and q: 'I will carry an umbrella', express the statement 'I will carry an umbrella only if it is raining' using a logical implication. Evaluate its truth when it is not raining.

   Hint

   Consider how the logical implication defines when the situation is false.

6. 6.

   Construct a truth table for the propositions p and q to show all outcomes of p | p ˄ q, q | p ⋁ q. Analyze which combinations yield true results.

   Hint

   Remember to fill out all combinations for true and false values.