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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).
Question 1: What is the minimum number of students each of whom comes from one of the 50 different states, enrolled in a university to guarantee that there are at least 100 who
The Ravens played 25 home games this year. They had 9 losses and 2 ties. How many games did they win? Eleven games are accounted for along with the losses and ties (9 + 2 = 11)
Positive Skewness - It is the tendency of a described frequency curve leaning towards the left. In a positively skewed distribution, the long tail extended to the right. In
Find out the area of the region enclosed by y = x 2 & y =√x . Solution Firstly, just what do we mean by "area enclosed by". This means that the region we're interested in
the value of y for which x=-1.5
Even and Odd Functions : This is the final topic that we have to discuss in this chapter. Firstly, an even function is any function which satisfies,
What is 2 5 ? 2 5 = 2 ×2 ×2 ×2 ×2 = 32
The Fourier series expansion for the periodic function, f ( t ) = |sin t | is defined in its fundamental interval. Taking π = 3.142, calculate the Fourier cosine series app
Newton's Second Law of motion, which recall from the earlier section that can be written as: m(dv/dt) = F (t,v) Here F(t,v) is the sum of forces which act on the object and m
the traffic light at three different road crossing change after every 48 seconds, 72 seconds and 108 seconds respectively. if they change simultaneously at 7 a.m., at what time wil
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