Linear regression

1. Construct the truth table for (p  q)  (¬p  q)

p q ¬p p  q ¬p  q (p  q)  (¬p  q)

2. Populate the truth table and see whether this statement is correct:

p  q ≡ ¬q  ¬q

p q p  q ¬ p ¬q ¬q  ¬q

3. Populate the provided truth table for the statement demonstrating De Morgan’s Law: ¬(p  q) ↔ ¬p V ¬q

p q

4. Use truth tables to show whether the following propositions are equivalent:

Proposition 1: p ∧ (q ∧ r)
Proposition 2: (q ∨ q) ∧ (q ∨ r)

p q r

5. For this logic circuit provide:
   a. the propositional logic formula
   b. the truth table. ¬ (A ∨ B)
   AND
   OR

A B C