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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).
Solve the subsequent IVP and find the interval of validity for the solution. y' + (4/x) y = x 3 y 2 , y(2) = - 1, x > 0 Solution Thus, the first thing that we re
Determine the equation of the plane that consists of the points P = (1, -2, 0), Q = (3, 1, 4) and R = (0, -1, 2). Solution To write down the equation of plane there is a re
Solving Algebraic Word Problems: What are the capacities of two water storage tanks in a nuclear facility if one holds 9 gallons less than three times another, and their whole
If a triangular sail has a horizontal length of 30 ft and a vertical height of 83 ft , Determine the area of the sail? a. 1,245 ft 2 b. 1,155 ft 2 c. 201 ft 2 d. 2,4
RATIONAL NUMBERS All numbers of the type p/q where p and q are integer and q ≠0, are known as rational. Thus it can be noticed that every integer is a rational number
If the p th term of an AP is q and the q th term is p. P.T its n th term is (p+q-n). Ans: APQ a p = q a q = p a n = ? a + (p-1) d = q a + (q-1) d = p
Characteristics of Time Series Time series has the given characteristics. a) A long term trend (T) -tendency of the whole series to fall and rise. b) Seasonal variati
Before searching at series solutions to a differential equation we will initially require to do a cursory review of power series. So, a power series is a series in the form, .
lcm method of 648
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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