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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 a rational number?
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Ratio Test In this part we are going to take a look at a test that we can make use to see if a series is absolutely convergent or not. Remind that if a series is absolutely c
1 1 1 1 1 2 1 2 ? and 40/2=? 2/40=?
Doing the following exercise will give you and opportunity to think about this aspect of children. E1) List some illustrations of exploration by four or five-year-olds that you
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