2.3.2. De Morgan's Law

Try these first

1. 1.

   Define tautology and give an example.

   Hint

   Think of a statement that cannot be false.

2. 2.

   What is a contradiction? Give an example.

   Hint

   Consider how you can have p true and false simultaneously.

3. 3.

   What do we call a statement that is always true?

   • A) Tautology
   • B) Contradiction
   • C) Contingency

   Hint

   This type of statement includes `p ∨ ¬p`.

4. 4.

   Is p ∧ ¬p a tautology?

   • True
   • False

   Hint

   What happens when p takes both true and false values?

5. 5.

   Using De Morgan's laws, prove that ¬(p ∧ q) is logically equivalent to ¬p ∨ ¬q. Include all logical steps.

   Hint

   Consider how negation would affect both components.

6. 6.

   Create a complex logical statement involving multiple variables and use logical identities to simplify and demonstrate equivalence.

   Hint

   Think of separating the conjunction over the disjunction and applying negation effectively.