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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).
give me the derivation of external division of sectional formula using vectors
Let a 0 , a 1 ::: be the series recursively defined by a 0 = 1, and an = 3 + a n-1 for n ≥ 1. (a) Compute a 1 , a 2 , a 3 and a 4 . (b) Compute a formula for an, n ≥ 0.
Characteristics of Exponential Smoothing 1. More weight is described to the most recent data. 2. All past data are incorporated not like in moving averages. 3. Les
Find out if each of the subsequent series are absolute convergent, conditionally convergent or divergent. Solution: (a) The above is the alternating harmonic ser
In polynomials you have seen expressions of the form x 2 + 3x - 4. Also we know that when an expression is equated to zero or some other expression, we cal
Let R be the relation on S = {1, 3, 6, 9, 27} defined by aRb iff a|b. (a) Write down the matrix of R. (b) Draw the digraph of R. (c) Explain whether R is reflexive, irrere
Steve Fossett is going the shores of Australia on the ?rst successful solo hot air balloon ride around the world. His balloon, the Bud Light Spirit of Freedom, is being escorted
if prices are calculatead with a 35% markup based on cost,what is the percent that those prices should be marked down to get back to their original cost?Choose any convenient cost
A family may deduct 24% of their childcare expenses from their income tax owed. If a family had $1,345 in childcare expenses, how much can they deduct? Find out 24% of $1,345 b
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