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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).
(a) Convert z = - 2 - 2 i to polar form. (b) Find all the roots of the equation w 3 = - 2 - 2 i . Plot the solutions on an Argand diagram.
Example of Rounding Off: Example: Round off the subsequent number to two decimal places. 6.238 Solution: Step 1: 8 is the number to the right of t
Consider the unary relational symbols P and L, and the binary relational symbol On, where P(a) and I(a) encode that a is a point and a (straight) line in the 2-dimensional space, r
Describe Segments, Rays, Angles, and Triangles We now define some more basic geometric figures. 1. Segments Definition A segment is the set of two given points and all the
Ravi is a teacher of Class 4 in a municipal school in Delhi. When the new school year started, he opened the textbook and started teaching the children how to write 4-digit numbers
100+5000
Activity This activity will help you recognize the importance of some very famous numbers, as well as learn more about approximations. Directions Using the Internet, provi
The two sides of a triangle are 17cm and 28cm long, and the length of the median drawn to the third side is equal to 19.5 cm. What is the distance from an endpoint of the median to
The amount of particulate matter left in solution during a filtering process is given by the equation p(n) = 500(2) -0.8n , where n is the number of filtering steps. Find the amoun
darien agrees to sponsor her sister $8 plus $1 for every mile she walks.Write an expression to show her total money
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