6.6.1. Part A

Try these first

1. 1.

   Express the statement, "You do not drive over 65 miles per hour," in terms of p.

   Hint

   Think about negation and what it means.

2. 2.

   What is the converse of the statement p → q?

   Hint

   Remember you switch the positions of the propositions.

3. 3.

   What does p → q indicate?

   • p implies q
   • q implies p
   • p and q are equivalent

   Hint

   Think of implications in everyday situations.

4. 4.

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

   • True
   • False

   Hint

   Recall the definition of contrapositive.

5. 5.

   Given the statements, "If it rains, I take an umbrella (p → q)," explain how its contrapositive helps understand the reasoning if the weather changes.

   Hint

   Reflect on how depending on actions shows understanding of conditions.

6. 6.

   Show through a truth table how p ⇔ q is equivalent to (p → q) ∧ (q → p).

   Hint

   Focus on the definition of biconditional.