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.
