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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).
Find out the absolute extrema for the given function and interval. g (t ) = 2t 3 + 3t 2 -12t + 4 on [-4, 2] Solution : All we actually need to do here is follow the pr
Example of Regression Equation An investment company advertised the sale of pieces of land at different prices. The given table shows the pieces of land their costs and acreag
sin 4 x - sin x = 0
Nora works at a laboratory as a chemist . she was told to prepare 100L of 25% alcohol solution. she has on hand of a 15% percent alcohol solution and a 40% alcohol solution which s
Question: Classify the following differential equations as linear/nonlinear. Also, what is the order of the following differential equations? Xy'-2y =x Xy'' -2y' =xsin(y)
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identify 4 sketch the quadric surfaces
Evaluate the subsequent integral. Solution This is an innocent enough looking integral. Though, because infinity is not a real number we cannot just integrate as norm
Find out the surface area of the solid acquired by rotating the following parametric curve about the x-axis. x = cos 3 θ y = sin 3 θ 0 ≤ θ ≤ ?/2 Solution We wil
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