6.6.2. Part B

Try these first

1. 1.

   What does the negation of p = 'It is sunny' mean?

   Hint

   Think about what it means to negate a statement.

2. 2.

   Translate the statement 'If it rains, then the ground is wet' into logical notation.

   Hint

   Identify the 'if' and 'then' parts in your statement.

3. 3.

   What logical connective indicates if-then relationships?

   • And
   • Or
   • Implies
   • Negates

   Hint

   Think about what happens in an if-then statement.

4. 4.

   Is the contrapositive of p → q logically equivalent to p → q?

   • True
   • False

   Hint

   Think about the structure of contrapositives.

5. 5.

   Prove that if p ↔ q and ¬q → r, then p → r is also valid.

   Hint

   Start with p ↔ q as two implications.

6. 6.

   If p is true, q as false, and r as true, determine the truth values for p → q, p ∨ r, and their implications.

   Hint

   Use truth assignments and verify for each operation.