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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).
what are cos and sin ?
Let f : R 3 → R be de?ned by: f(x, y, z) = xy 2 + x 3 z 4 + y 5 z 6 a) Compute ~ ∇f(x, y, z) , and evaluate ~ ∇f(2, 1, 1) . b) Brie?y
Solve the subsequent IVP. y′′ + 11y′ + 24 y = 0 y (0) =0 y′ (0)=-7 Solution The characteristic equation is as r 2 +11r + 24 = 0 ( r + 8) ( r + 3) = 0
How is the probability distribution of a random variable constructed? Usually, the past behavior of the variable is studied and the frequency distribution of the past data is form
What is equivalence relation? Prove that relation 'congruence modulo' ( ≡mod m) is an equivalence relation. Ans: A relation R illustrated on a nonempty set A is said to be
On a canoe trip. a person paddled upstream against the current ata an average of 2mi/h. the return trip with the current at 3mi/h. Need to find the paddling spped in still water an
Definition of a Function Now we need to move into the second topic of this chapter. Before we do that however we must look a quick definition taken care of.
I need help for Solving Equations by Completing the Square Method, can anybody help me out for this?
limit x APProaches infinity (1+1/x)x=e
WHAT IS PRECALC
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