Using the rules of propositional logic provided

2. Use propositional logic to prove the validity of the following arguments. (a) (P+Q) + (Q + P') (b) [(PAQ) + R] [P+(Q + R)] RULES OF PROPOSITIONAL LOGIC (Terminology and notation as per J. Gersting Mathematical Structures for Computer Science) Equivalence Rules Equivalent to Name/Abbreviation for Rule QVP Commutative comm QAP PVQVR) Associative assc PA(QAR) (PVQA (PVR) Distributivedist (PAQ) V (PAR) Identity-id Expression PVQ PAQ (PVQVR (PAQ AR PVQAR) PA(QVR) PVO PA1 PvP PAP' (PV) (PAD)' P Q (P) PVP PAP Peg Complement-comp De Morgan's Laws -DM P'Q' P'VQ PVQ Implication-imp | Double negation dn Simplification simp ( PQ) AQ +P) Definition of equivalence-equ Q From P, P Q P+Q, Q' P, Q PAQ Inference Rules Can Derive Name/Abbreviation for Rule Modus ponensmp Modus tollensmt PAQ Conjunction-con P, Q Simplification sim PVQ Addition-add P R Hypothetical syllogism-hs PQ, Q R