Mathematics

Mathematics

Senin, 24 September 2012

PR KELOMPOK


TUGAS KELOMPOK 9 PDM
Rombel 3
  1. Buktikan!
[ (pÙq) Ùp] Þq ek T
Jelas
~ [ (pÙq) Ùp]  Vq                    (Hk. Implikasi)
Û    ~ [~ (pÙq) V ~ p]  Vq             (Hk. DM)
Û    ~ [ (~pV~q) V~p]  Vq                        (Hk. DM)
Û    ~p V (~qV~p)   Vq                 (Hk. Asosiatif)
Û    ~p V (~pV~q)   Vq                 (Hk. Komutatif)
Û     (~pV~p) V~q Vq                   (Hk. Asosiatif)
Û    ~pV~qVq                                (Hk. Idempoten)
Û    ~PvT                                       (Hk. Komplement)
Û    T                                              (Hk. Identitas))

  1. [(pÞq) Ùp] Þq
Jelas
Û    [(~pVq) Ùp] Þq
Û     ~ [(~p Vq) Ùp] Vq
Û     [~ (~pVq) V~p] Vq
Û     [ (pV~ q) V~p] Vq
Û     [ (~qV p) V~p] Vq
Û     [ ~qV (p V~p)] Vq
Û     (~qV T) Vq
Û     TV(~q Vq)
Û    TvT
Û    T

  1. [ (pÞq) Ù ~q ] Þ ~p
Jelas
Û     [ (~p Úq) Ù~q ]  Þ ~p
Û     [ (~pÚq) Ù ~q] Ú ~p
Û     [(~pÚ~q) Ú~q] Ú~p
Û     [pÚ~q) Úq] Ú~p
Û     [pÚ(~pÚq)] Ú~p
Û     (pÚT) Ú~p
Û     T Ú(pÚ~p)
Û     TÚT
Û     T
  1. Corresponding to the statement 'neither X nor Y', the joint negation X ¯ Y is defined by the truth table
Show that (i) X ¯ Y eq ~ (X v Y) and (ii) X eq (X ¯ X) ¯ (X ¯ X).
~X
X
¯
X
F
T
F
T
T
F
T
F
F
T
F
T
T
F
T
F

X
Ú
Y
X
¯
Y
¯
X
¯
Y
T
T
T
T
F
T
T
T
F
T
F
T
T
F
F
T
T
F
F
T
T
T
F
T
F
F
T
T
F
T
F
T
F
F
T
F
F
F
T
F




  1. . Show that (i) ~X eq X ¯ X and (ii) X v Y eq (X ¯ Y) I (X¯i Y). From these results find the equivalent formulae of X Ù Y, X -*® Y and AT« Y as iterated compositions of joint negations.
~
(X
Ú
Y)
F
T
T
T
F
F
T
T
F
T
T
F
T
F
F
F

(X
¯
X
¯
(X
¯
X)
T
F
T
T
T
F
T
F
T
F
F
F
T
F
T
F
T
T
T
F
T
F
T
F
F
F
T
F