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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).
Convert measurements between the English system? To convert measurements between the English system and the metric system: 1. Look up the conversion between the two units of
If the squared difference of the zeros of the quadratic polynomial x 2 + p x + 45 is equal to 144 , find the value of p.
Suppose S = {vi} and T = {ti} are "easy" sets of knapsak weight. Also, P and q are primes p > ?Si and q > ?ti. We can combine S and T into a signle set of knapsack weight as follow
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
An unbiased die is tossed twice .Find the probability of getting a 4,5,6 on the first toss and a 1,2,3,4 on the second toss
Factoring By Grouping It is a method that isn't utilized all that frequently, but while it can be used it can be somewhat useful. Factoring by grouping can be nice, however it
prove That J[i] is an euclidean ring
Town x and town y were 270km apart. a car started from town x towards town y at a uniform speed of 60km/hr, while a motorcycle started from town y to town x at a uniform speed of 9
Find the common difference of an AP whose first term is 100 and sum of whose first 6 terms is 5 times the sum of next 6 terms. Ans: a = 100 APQ a 1 + a 2 + ....... a 6
The graph C n , n ≥ 3 contains n vertices and n edges creating a cycle. For what value of n is C n a bipartite graph? Draw the bipartite graph of C n to give explanation for yo
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