6.8.4. Duals of Logically Equivalent Statements

Try these first

1. 1.

   What is the negation of p?

   Hint

   Think about the opposite of the statement represented by p.

2. 2.

   What does p → q mean?

   Hint

   It's an implication, so consider the relationship between p and q.

3. 3.

   What is the negation of p → q?

   • ¬p → q
   • p → ¬q
   • ¬(p → q)

   Hint

   Consider how negation affects the entire statement.

4. 4.

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

   • True
   • False

   Hint

   Remember what contrapositive entails.

5. 5.

   Prove that if p → q and q → r are true, then p → r is also true.

   Hint

   Consider the chain of implications between p, q, and r.

6. 6.

   If the dual of a compound statement is identical to its original, what can you infer?

   Hint

   Think about which types of statements maintain structure and cannot be altered.