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Consider a database whose universe is a finite set of vertices V and whose unique relation .E is binary and encodes the edges of an undirected (resp., directed) graph G: (V, E). Each undirected edge between the nodes o and u (resp., directed edge from the node v to the node u) is encoded by the two atoms E (v, u) and E (u, v) (resp., by the single atom E (v, u)).
Consider the pairs of stucture (undirected (resp., directed) graphs) shown in Fig. 1. Suppose that the graphs are encoded in a database as explained above. For each pair, answer the following questions:
1. What is the smallest quantifier rank k for which the spoiler wins the k-move Ehrenfeucht-Fraisse game on the pair of structure?
2. Derive a Boolean first-order query from your winning strategy that is true on one structure but not on the other (you can use the equality relation between vertices).
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An experiment designed to test the potency of a drug on 20 rats. Last animal studies have shown that a 10 mg dose of the drug is lethal 5% of the time within the first 4 hours; of
If a+b+c = 3a , then cotB/2 cotC/2 is equal to
x/15=50/20
A plane is flying at 200 mph with a heading of 45degrees and encounters a wind mph from the west. What is the velocity and heading?
Rolle's Theorem Assume f(x) is a function which satisfies all of the following. 1. f(x) is continuous in the closed interval [a,b]. 2. f(x) is differentiable in the ope
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(a) An unordered pair fm; ng with 1 ≤ m ≠ n ≤ 6 is called a duad. List the 15 duads. (b) There are 15 ways to partition {1, ......, 6 } into 3 duads, such as { {1; 2}, {3, 4},
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