Hello, I would like to solve these questions in detail today, please

1. Prove that p q (pq) (pq) are logical equivalent without using a truth table.
2. Show that ((p q) p) q is a tautology without using a truth table.
3. Show that (pq) q p q are logical equivalent without using a truth table.
4. Prove that [(p q) p] q is a tautology without using a truth table.
5. Show that (p q) (q r) (p r) is a tautology without using truth table.