Explain the logical structure of the following set of
propositions - a theory.
1.The set of languages accepted (decided) by deterministic
Turing machines = the set of languages accepted (decided) by
nondeterministic Turing machines
2. PATH belongs to P
3. TAUTOLOGY is a member of coNP
4. 2 definitions for NP (1 in terms of a polynomial verifier 2
in terms of a nTM) are equivalent
5. PSPACE = NPSPACE
6. NP is a subset of PSPACE
7. SAT belongs...
Explain if the set below is a vector space given standard
operations.
The set of all even functions defined on R with addition and scalar
multiplication defined as follows:
1.) (f+g)(x) = f(x) + g(x) (addition)
2.) (cf)(x) = cf(x)
Which of the following are valid relationships in set theory?
Explain why or why not.
(a) (A or B or C)' = A' or B'
or C'
(b) A or B or C = A or (A' and
B) or [[A or (A' and B)]' and C]
(c) (A or B) and (A' or B') =
(A and B') or (A' and B) or (A' and B and C')
(d) (A and B) or (A and...