6.4. Question 3

Try these first

1. 1.

   Create a truth table for the proposition p → q.

   Hint

   Remember to note when `p` being true and `q` being false is the only situation that makes `p → q` false.

2. 2.

   What does ¬ p represent?

   Hint

   Think of it as 'not p'.

3. 3.

   What is the only situation where p → q is false?

   • When both are true
   • When `p` is true and `q` is false
   • When both are false

   Hint

   Think about the conditional relationship.

4. 4.

   Is p ↔ q true if both p and q are false?

   • True
   • False

   Hint

   Consider the definition of bi-implication.

5. 5.

   Construct a complete truth table for the expression ((p → q) ∧ (¬ p → r)) ↔ (q ∨ r).

   Hint

   Check each part incrementally, ensuring you're capturing the implications accurately.

6. 6.

   Prove using truth values that (p → q) -> (¬ q → ¬ p) is a tautology.

   Hint

   Focus on filling out the truth values for both sides and comparing.