6.6. Question 5

Try these first

1. 1.

   Define a propositional variable in your own words.

   Hint

   Think of variables in mathematics.

2. 2.

   What does a bi-implication mean?

   Hint

   It's about mutual truthfulness.

3. 3.

   What does it mean for a set of propositions to be consistent?

   • They can all be true at the same time
   • They contradict one another
   • None of the above

   Hint

   Think about truth values.

4. 4.

   If p ↔ q is true, and p is false, what must q be?

   • True
   • False

   Hint

   Refer to the definition of bi-implication.

5. 5.

   Prove that the conjunction of p ↔ q and q → r leads to a consistent specification if r is also Implied by p.

   Hint

   Sketch the implication chain to visualize.

6. 6.

   Create a truth table for expressions p → q and ¬r, determining if their conjunction is satisfiable.

   Hint

   Remember to check all combination rows thoroughly.