6.7.2. Part B

Try these first

1. 1.

   What is the negation of p?

   Hint

   Think of the opposite of the statement represented by p.

2. 2.

   Write the converse of p → q.

   Hint

   Just flip the order of the original implication.

3. 3.

   What does the statement p ↔ q mean?

   • p is true if q is true
   • p implies q
   • q is necessary for p

   Hint

   Think about when both conditions agree.

4. 4.

   If p is false, what is the truth value of p → q?

   • True
   • False

   Hint

   Check the rules for implications.

5. 5.

   Create a complex logical statement using at least three propositional variables. Write the statement out and then construct a truth table for it.

   Hint

   Use systematic methods for combining truth values.

6. 6.

   Prove that (p → q) ∧ (¬q → ¬p) is logically equivalent to p ↔ q by showing both sides have the same truth values.

   Hint

   Detailed comparisons of truth values will help.