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| Mind Map BAB 1 Bag.2 |
Mathematics
Rabu, 26 September 2012
Senin, 24 September 2012
PR KELOMPOK
TUGAS
KELOMPOK 9 PDM
Rombel
3
- 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))
- [(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
- [ (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
- 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
|
- . 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
|
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