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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).
SUMMATION NOTATION Under this section we require to do a brief review of summation notation or sigma notation. We will start out with two integers, n and m, along with n a
We know that the terms in G.P. are: a, ar, ar 2 , ar 3 , ar 4 , ................, ar n-1 Let s be the sum of these terms, then s = a + ar + ar 2
How to Find the range of a function ? Sigh. Students ask me this all the time. They don't want an explanation, they want a procedure. "Tell me the steps!" Unfortunately, th
Rejection and Acceptance regions All possible values which a test statistic may either suppose consistency along with the null hypothesis as acceptance region or lead to the re
Minimum and Maximum Values : Several applications in this chapter will revolve around minimum & maximum values of a function. Whereas we can all visualize the minimum & maximum v
By the method of completion of squares show that the equation 4x 2 +3x +5 = 0 has no real roots. Ans: 4 x 2 +3 x +5=0 ⇒ x 2 + 3/4 x + 5 = 0 ⇒ x 2 + 3/4 x +
#questi0+50x1-60-60x0+10on..
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Euler''''s Constant (e) Approximate the number to the one hundredth, one ten-thousandths, and one one-hundred-millionth.
how do you divide
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