Question

( p ∧ q) ∧ ( p ∨ q ) ≡ p solution by laws of logical equivalence

Answer 1

The solution by laws of logical equivalence to (p ∧ q) ∧ (p ∨ q) is p ∨ q.

Step-by-step explanation:

The solution to the logical equivalence is as follows:

1. Start with the expression ( p ∧ q) ∧ ( p ∨ q ).
2. Apply the distributive law: ( ( p ∧ q ) ∧ p ) ∨ ( ( p ∧ q ) ∧ q ).
3. Apply the associative law: ( p ∧ ( q ∧ p ) ) ∨ ( q ∧ ( p ∧ q ) ).
4. Apply the identity law: p ∨ q.

Therefore, ( p ∧ q) ∧ ( p ∨ q ) is equivalent to p ∨ q.