2. Discrete Mathematics

Try these first

1. 1.

   What is a tautology? Give an example.

   Hint

   Think of a logical disjunction that includes both a variable and its negation.

2. 2.

   Define contradiction and provide an example.

   Hint

   Consider a logical conjunction that cannot logically be true.

3. 3.

   What is the definition of a tautology?

   • A statement that is always false
   • A statement that is sometimes true
   • A statement that is always true

   Hint

   Think of a logical expression that is universally true.

4. 4.

   Is the statement 'p ∧ ¬p' a contradiction?

   • True
   • False

   Hint

   Consider the logical compatibility of p and its negation.

5. 5.

   Prove that ¬(p ∨ q) is logically equivalent to ¬p ∧ ¬q.

   Hint

   Recall how negation interacts with disjunctions.

6. 6.

   Show that (p → q) ↔ (¬q → ¬p) using a truth table.

   Hint

   Typical truth tables can help clarify the relationships between implications.