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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).
If the points (5, 4) and (x, y) are equidistant from the point (4, 5), prove that x 2 + y 2 - 8x - 10y +39 = 0. Ans : AP = PB AP 2 = PB 2 (5 - 4) 2 + (4 - 5) 2 = (x
Finding the Inverse of a Function : The procedure for finding the inverse of a function is a rather simple one although there are a couple of steps which can on occasion be somewh
Question: Find the quotient and remainder when f(x) = x 5 - x 4 - 4x 3 + 2x + 3 is divided by g(x) = x-2. Make sure the quotient and remainder are clearly identified.
5/7+5/14
Evaluate the given limit. Solution: In this question none of the earlier examples can help us. There's no factoring or simplifying to accomplish. We can't rationalize &
Determine the height of the Washington Monument to the nearest tenth of a meter. a. 157.8 m b. 169.3 m c. 170.1 m d. 192.2 m c. The height of the monument is the add
The product of -7ab and +3ab is (-7 x 3) a 2 b 2 = -21a 2 b 2 . In other words, a term with minus sign when multiplied with a term having a positive sign, gives a product having
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
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The Shape of a Graph, Part I : In the earlier section we saw how to employ the derivative to finds out the absolute minimum & maximum values of a function. Though, there is many
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