Foundations of Computer Science_Homework 1A

Foundations of Computer Science: Honors 
Homework 1A
Problem 1
Write P =⇒ Q using ∧ and ¬. Show that your two representation are equivalent. 

Problem 2 Prove that the prepositional formulas
P ∨ Q ∨ R
and
(P ∧¬Q) ∨ (Q ∧¬R) ∨ (R ∧¬P) ∨ (P ∧ Q ∧ R)
are equivalent.

Problem 3 (a) Write the biconditional ( ⇐⇒ ) using only implies ( =⇒ ) and and (∧). Prove that the new version is equivalent. (b) Write it using only ∨ and ¬. Show your derivation.