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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).
what is the length of a line segment with endpoints (-3,2) and (7,2)?
Oscar's Oil Company provides customers a 5% discount if they pay their bill within 10 days. The Stevens' oil bill is $178. How much do they save if they pay the bill inside 10 days
love is a parallelogram where prove that is a rectangle
if oranges are bought at the rate of 11 for rupees 10 and are sold at the rate of 10 for rupees 11, find the profit percent
Properties of Cross product If u, v and w are vectors and c is a number then u → * v → = -v → * w → (cu → ) * v → =
two colum proofs
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Any point on parabola, (k 2 ,k) Perpendicular distance formula: D=(k-k 2 -1)/2 1/2 Differentiating and putting =0 1-2k=0 k=1/2 Therefore the point is (1/4, 1/2) D=3/(32 1/2
Hydrostatic Pressure and Force - Applications of integrals In this part we are going to submerge a vertical plate in water and we wish to know the force that is exerted on t
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