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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).
Evaluate following integrals. ( (1 - (1 /w) cos (w - ln w) dw Solution In this case we know how to integrate only a cosine therefore let's makes th
program sample for proportion
There may be more than one independent variable which determines the value of y. The dimension of a function is determined by the number of independent variables in the
dterminant order 3*3
how to know if it is function and if is relation
1) At a midway game at the state fair, the probability of winning an individual game is advertised to be 30% ( p = . 3). Suppose 50 people played the game (assume all 50 outcomes
Find the acute angle theta that satisfies the given equation. Give theta in both degrees and radians. You should do these problems without a calculator. Sin= sqroot3/2
A juicer is available for 3500 cash but was sold under installment plan where the purchaser agreed to pay 1500 cash down and 3 equal quarterly installments. If the dealer charges i
show that one of the straight lines given by ax2+2hxy+by2=o bisect an angle between the co ordinate axes, if (a+b)2=4h2
In the innovations algorithm, show that for each n = 2, the innovation Xn - ˆXn is uncorrelated with X1, . . . , Xn-1. Conclude that Xn - ˆXn is uncorrelated with the innovations X
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