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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).
How to Dividing Rational Expressions ? To divide two fractions, or rational expressions, keep in Mind that division is the same as multiply by the Reciprocal of the second fra
The price of heating oil rose from $1.10 per gallon to $1.43 per gallon. What is the percent of increase? The price of heating oil rose $0.33 ($1.43 - $1.10 = $0.33). To ?nd ou
Find the 35th term of the sequence in which a1 = -10 and the common difference is 4.
Rates of Change and Tangent Lines : In this section we will study two fairly important problems in the study of calculus. There are two cause for looking at these problems now.
Lines- Common Polar Coordinate Graphs A few lines have quite simple equations in polar coordinates. 1. θ = β We are able to see that this is a line by converting to Car
Solve the recurrence relation T (K) = 2T (K-1), T (0) = 1 Ans: The following equation can be written in the subsequent form: t n - 2t n-1 = 0 Here now su
According to a Gallup poll 51% of US women prefer to have a job outside of the home. What is the chance that a survey of 200 women would find that 45% or less of the respondants
how much congruent sides does a trapezoid have
If arg (a/b) = pi/2, then find the value of ((a+b)/(a-b)) where a,b are complex numbers. Ans) Arg (a/b) =Pi/2 Tan-1 (a/b)= Pi/2 A/B = tanP/2 ,therefore a/b=infinity.
Pat is making a Christmas tree skirt. She needs to know how much fabric to buy. Using the example provided, calculate the area of the skirt to the nearest foot. a. 37.7 ft 2
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