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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).
Finding the Slope of a Line, Given Two Points on it ? Find the slope of the line passing through the pairs of points (-5, -2) and (2, 4). One way to find the slope is
(a) Determine the matrix that first rotates a two-dimensional vector 180° anticlockwise, and then per- forms a horizontal compression of the resulting vector by a factor 1/2 (leavi
about scalene,equilateral and isosceles.
What is Matrices?
Indeterminate form : The 0/0 we initially got is called an indeterminate form. It means that we don't actually know what it will be till we do some more work. In the denominator
Parametric objective-function problems
Rules Of Game Theory i. The number of competitors is finite ii. There is conflict of interests among the participants iii. Each of these participants has available t
Chain Rule : Assume that we have two functions f(x) & g(x) and they both are differentiable. 1. If we define F ( x ) = ( f o g ) ( x ) then the derivative of F(x) is,
Each week Jaime saves $25. How long will it take her to save $350? Divide $350 by $25; 350 ÷ 25 = 14 weeks.
what is the difference between North America''s part of the total population and Africa''s part
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