Question

A Theorem 3.2. Suppose P, R and S are atomic propositions. Then the propositional form appearing in column A is logically equivalent to the corre- sponding propositional form in Column B. В. POR ( P R ) ^ (R=P). ~(PvR) (~P) ^ (~ R) ~(PAR) (~ P) v (~ R) ~( PR) P^~R ~(PAR) P=R P^(RVS) (PAR) v (PAS) Pv(RAS) (P v R) ^ (PVS) While the importance of the equivalent propositional forms stated in The- orem 3.2 are important, most can be easily remembered without much diffi- culty. Readers are asked to examine each equivalency to acquire the reasoning behind their equivalency.

Answer 1

PAR PAR ( PR) a (RAP) P R RAP PAR T T T T T F T F (PAR) (RAR) T druta Ittt tatt F T IPVR) P P R (PUR) TT T T F T F T T F F F at tus ttt 4 tout at ttt R R P InP) Al T T F F F T & T F F F T F T F FIT T T +T7 F (~P) ( ~R) attuu tttt 7 ~ (PAR) P R PAR ~ (POR) P R ~P aR TT TF T F F T F T F T FT T F FF FT F T T T. ~(PR) - PA ~R P R RR- ~(PAR) P R AR POR TT 7 F T T F F T F F + TO FT AT FT of FFT ortut FT T F FT 나ㅏ ㅑ TTT 1) م ~ (PAR) P R PAR "PAR) TT Troits F TF f T. FT F F F F PYNR. P R nR PYAR mi T T F of T F T T FT E خ arrt FF T

P ACRYS) (RVS) PACRYS) + + F tatt T + BF F T T rrrrrrrr ) & TT TT t t. TT T PAR) V P R T T (PAS) S PAR T PAS (PAR) V (PAS) TATTttto rt att ut TTTTTTT+ KTP TTTT TTTTTtttu T F T P F RAS pv (RAS) PV CRAS) P R S T T T ТТЕ at ttuttt ntttttttt TATT ttttttt FT F f (PUR) Prs) P R S PYR T T T Т ТЕТ T F T T F F PYS (PYR) M (PVS) TTTTtttton errrrrrr tttttutu + F TF