7.2.4. Negation and Disjunction Functionality

Try these first

1. 1.

   What is the definition of a conjunction?

   Hint

   Think about the word 'and'.

2. 2.

   How is negation represented in logical expressions?

   Hint

   It flips the truth value.

3. 3.

   Which of the following operators can be considered functionally complete?

   • Only conjunction
   • Only disjunction
   • Conjunction and negation
   • Disjunction and implication

   Hint

   Think about what operators connect all statements.

4. 4.

   True or False: Negation reverses the truth value of a proposition.

   • True
   • False

   Hint

   Consider what happens when you say not true.

5. 5.

   Given the expression p ↔ q, demonstrate how to express it using only conjunction and negation.

   Hint

   Remember to break down the implications!

6. 6.

   Show that the expression ¬(p ∧ q) is equivalent to ¬p ∨ ¬q using transformations.

   Hint

   It's about negating prior outcomes.