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Mathematical Proofs

   

Added on  2019-09-26

12 Pages1564 Words348 Views
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Ans:a)PQ(P VQ)!P(!P -> Q)(P V Q) <-> (!P -> Q)TTTFTTTFTFTTFTTTTTFFFTFTb)PQ(P -> Q)!P!Q!Q -> !P(P -> Q) ^ (!Q->!P)(Q ->P)((P -> Q) ^ (!Q->!P) )-> (Q ->P)TTTFFTTTTTFFFTFFTTFTTTFTTFFFFTTTTTTTc)PQ(P VQ)!Q(P V Q) ^ !Q((P V Q) V^!Q ) - > PTTTFFTTFTTTTFTTFFTFFFTFT
Mathematical Proofs_1

d)PQ(P -> Q)(P -> Q) ^ P((P -> Q ) ^ P )-> QTTTTTTFFFTFTTFTFFTFTAns: a)PQRP V Q(P V Q) -> R!P(Q V R)!P <-> (Q V R)((P V Q) -> R) ^ (!P <-> (QV R))TTTTTFTFFTTFTFFTFFTFTTTFTFFTFFTFFFTFFTTTTTTTTFTFTFTTTTFFTFTTTTTFFFFTTFFF
Mathematical Proofs_2

b) PQRQ V RP ^ (QV R)P ^ QP ^ R(P ^ Q) V (P ^ R)((P^(Q V R)) <-> ((P^Q V (P ^ R))TTTTTTTTTTTFTTTFTTTFTTTFTTTTFFFFFFFTFTTTFFFFTFTFTFFFFTFFTTFFFFTFFFFFFFFTAns:
Mathematical Proofs_3

Mathematical Proofs_4

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