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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).
A rectangular container is 15 cm wide and 5 cm long, and contains water to a depth of 8 cm. An object is placed in the water and the water rises 2.3 cm. Determine the volume of the
Note that there are two possible forms for the third property. Usually which form you use is based upon the form you want the answer to be in. Note as well that several of these
Is prerequisite multipcation or addition
(19 + 7 i)
The height of a rectangle is 20 cm. The diagonal is 8 cm more than the length. Determine the length of the rectangle. a. 20 b. 23 c. 22 d. 21 d. To determine the len
Consider a person's decision problem in trying to decide how many children to have. Although she cares about children and would like to have as many as possible, she knows that chi
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Assume that i) Determine all the roots of f(x) = 0. ii) Determine the value of k that makes h continuous at x = 3. iii) Using the value of k found in (ii), sh
Kyra receives a 5% commission on every car she sells. She received a $1,325 commission on the last car she sold. What was the cost of the car? Use the proportion part/whole =
Classifying critical points : Let's classify critical points as relative maximums, relative minimums or neither minimums or maximums. Fermat's Theorem told us that all relative
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