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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).
darien agrees to sponsor her sister $8 plus $1 for every mile she walks.Write an expression to show her total money
Solve the subsequent IVP and find the interval of validity for the solution xyy' + 4x 2 + y 2 = 0, y(2) = -7, x > 0 Solution: Let's first divide on both
Let 0 ! V1 ! ! Vk ! 0 be a long exact sequence of vector spaces with linear maps. Show that P (??1)i dim Vi = 0.
With a compass draw the arc associated with a 720° angle, it looks like a circle. With a protractor, label the angle in multiples of 45° and 30° up to 720°. Notice 30° and 390° ar
Five years ago a business borrowed $100,000 agreeing to repay the principal and all accumulated interest at 8% pa compounded quarterly, 8 years from the loan date. Two years after
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Definition Assume that f(t) is a piecewise continuous function. The Laplace transform of f(t) is denoted L{ f (t )} and defined by, There is an optional notation for L
Properties of Cross product If u, v and w are vectors and c is a number then u → * v → = -v → * w → (cu → ) * v → =
Advantages and disadvantages of operation researchs
Circles - Common Polar Coordinate Graphs Let us come across at the equations of circles in polar coordinates. 1. r = a . This equation is saying that there is no matter
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