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Laws of Logic

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									Roll No.1255                        Bio-Informatics    5th Semester(M)


                                LAWS of Logic
    1. Double Negation Law:[           ]

P ¬P ¬(¬P)
T F    T
F T     F
  2. Negation law:[P V ¬        &            ]

P ¬P PV¬P PΛ¬P
T F     T       F
F T     T       F
  3. Negation of t & c:         &

P ¬P PV¬P=t PΛ¬P=c ¬t ¬c
T F      T          F   T F
F T      T          F   T F
  4. Identity law:[PΛ t  &

P t       c PV¬c PΛ¬t
T T       F   T       T
F T       F   F       F
  5.      Idempotent Law:           & PV

P PVP PΛP
T  T     T
F   F    F
  6. Universal Found Law:             t&         c]

P t       c PVt PΛc
T T       F T      F
F T       F T      F
     7.   Cumulative Law:[(i)
(i)
P Q       PΛQ QΛP
T T        T   T
T F        F   F
F T        F   F
F F        F   F
(ii)
P Q       PVQ QVP
T T        T   T
T F        T   T
F T        T   T
F F        F   F


1st Assignment                  Discrete Mathematics       08/10/2009
Roll No.1255                 Bio-Informatics      5th Semester(M)


    8. Associative Law:
(i)
P Q       r PΛQ QΛr (PΛQ)Λr PΛ(QΛr)
T T       T  T   T     T       T
T T       F  T   F     F       F
T F       T  F   F     F       F
T F       F  F   F     F       F
F T       T  F   T     F       F
F F       T  F   F     F       F
F T       F  F   F     F       F
F F       F  F   F     F       F
(ii)
P Q       r PVQ QVr (PVQ)Vr PV(QVr)
T T       T     T      T     T T
T T       F     T      T     T T
T F       T     T      T     T T
T F       F     T      F     T T
F T       T     T      T     T T
F F       T     F      T     T T
F T       F     T      T     T T
F F       F     F      F     F F
     9.   Distributive Law:[                                  ]
(i)
P Q       r PΛQ PΛr QVr PΛ(QVr) (PΛQ)V(PΛr)
T T       T  T   T   T     T         T
T T       F  T   F   T     T         T
T F       T  F   T   T     T         T
T F       F  F   F   F     F         F
F T       T  F   F   T     F         F
F F       T  F   F   T     F         F
F T       F  F   F   T     F         F
F F       F  F   F   F     F         F
(ii)
P Q       r PVQ PVr QΛr PV(QΛr) (PVQ)Λ(PVr)
T T       T  T   T   T     T         T
T T       F  T   T   F     T         T
T F       T  T   T   F     T         T
T F       F  T   T   F     T         T
F T       T  T   T   T     T         T
F F       T  F   T   F     F         F
F T       F  T   F   F     F         F
F F       F  F   F   F     F         F




1st Assignment             Discrete Mathematics       08/10/2009
Roll No.1255                   Bio-Informatics              5th Semester(M)


   10. Demorgan’s Law:[(i)        ¬PV¬Q (ii) ¬(P        ]
(i)
P Q PΛQ ¬(PΛQ) ¬P ¬Q ¬PV¬Q
T T       T        F      F F F
T F       F        T      F T T
F T       F        T      T F T
F F       F        T      T T T
(ii)
P Q PVQ ¬(PVQ) ¬P ¬Q ¬PΛ¬Q
T T       T        F      F F F
T F       T        F      F T F
F T       T        F      T F F
F F       F        T      T T T
     11. Absorption Law:[                           ]
(i)
P PΛP PV(PΛP)
T     T        T
F     F        F
(ii)
P PVP PΛ(PVP)
T     T        T
F     F        F




1st Assignment               Discrete Mathematics               08/10/2009

								
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