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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).
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define regular pyramid
Trapezoid Rule - Approximating Definite Integrals For this rule we will do similar set up as for the Midpoint Rule. We will break up the interval [a, b] into n subintervals of
explanation
a ,b,c are complex numbers such that a/1-b=b/1-c=c-1-a=k.find the value of k
Assumptions The figures known are assumed to be a normal series, that is a series without any violent, unexplained fluctuations in the values. The
Determine how many square centimeters of paper are needed to make a label on a cylindrical can 45 cm tall with a circular base having diameter of 20 cm. Leave answer in terms of π.
Let Xn be a sequence of distinct real numbers. Defi ne E = {L : L is a subsequential limit of Xn}. Prove E is closed.
Basic indefinite integrals The first integral which we'll look at is the integral of a power of x. ∫x n dx = (x n +1 / n + 1)+ c, n
Graph A graph G = (V, E) contains a (finite) set that is denote by V, or by V(G) if one wishes to make clear which graph is under consideration, and a collection E, or E(G), o
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