6.1. Discrete Mathematics

Try these first

1. 1.

   What does the negation of the statement 'p' represent?

   Hint

   Think of it as contrary to the truth of 'p'.

2. 2.

   How many possible truth values are there for two propositions?

   Hint

   Consider the truth outcomes for each proposition combined.

3. 3.

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

   • True
   • False

   Hint

   Remember the definition of an implication.

4. 4.

   Is ¬(p ∨ q) logically equivalent to ¬p ∧ ¬q?

   • True
   • False

   Hint

   Think about how negation distributes over disjunction.

5. 5.

   Create a compound proposition using p, q, and r that reflects a real-world scenario, then provide its truth table.

   Hint

   Break down each scenario to see the impacts of each proposition.

6. 6.

   Prove the logical equivalence between the statements p → q and ¬q → ¬p by constructing truth tables.

   Hint

   Ensure to cover all combinations in your truth tables.