6.7. Question 6

Try these first

1. 1.

   What is the logical form of 'if it rains, the ground will be wet'?

   Hint

   Identify the main components of the statement.

2. 2.

   What does p → q mean?

   Hint

   Think about how you would express a cause-and-effect relationship.

3. 3.

   Which of the following represents an implication?

   • p ∧ q
   • p ∨ q
   • p → q

   Hint

   Look for the statement indicating a conditional relationship.

4. 4.

   True or False: The contrapositive of p → q is p → ¬q.

   • True
   • False

   Hint

   Recall what 'contrapositive' means.

5. 5.

   Prove that (p ∧ q) → r is logically equivalent to ¬p ∨ ¬q ∨ r using a truth table.

   Hint

   Focus on every combination of truth values for p, q, and r.

6. 6.

   Demonstrate the non-equivalence of (p → q) and (q → p) and justify your answer.

   Hint

   Consider scenarios that reveal their truth values.