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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).
Look on the web for a data base that can be converted to an undirected graph. For example, in Science there is a data base of proteins and their interactions. Each protein can b
Substitution Rule for Definite Integrals Now we need to go back and revisit the substitution rule as it also applies to definite integrals. At some level there actually isn't
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provide a real-world example or scenario that can be express as a relation that is not a function
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4.2^2x+1 - 9.2^x + 1=0
Suppose that x = x (t ) and y = y (t ) and differentiate the following equation with respect to t. Solution x 3 y 6 + e 1- x - cos (5
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