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Homework CISC 2
Due on Thursday, March 18, 2010
1. Show
res ((AB ) (B C ))((C A)B ).
b. {((A B ) (C D))} res ((A (C D)) (B (C D)))
a.
c. {((C B )B ), (C A), ((B C )A)} res (B C ).
2. You may use any of the Theorems/Lemmas/Propositions from the text book up through
Proposition 1.12 regarding axiomatic theory L while answering this question. In this question, is a set of wfs.
a. is said to be L-inconsistent for if some wf, ,
is L-inconsistent then for any statement form ,
as well as
L .
L
L
. Show that if
b. We say is L-complete if for each , L or L . Assume is L-complete. Show
that
(i) if L ( ) then L or L .
(ii) if L ( ) then L and L .
c. Show that if
d. Show
L
L
i for 1 i n and {1 , . . . , n } |= then
(AB )((C A)(C B )).
e. Show that if {}
L
then { }
L
1
.
L
.