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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).
The line 4x-3y=-12 is tangent at the point (-3,0) and the line 3x+4y=16 is tangent at the point (4,1). find the equation of the circle. solution) well you could first find the ra
Determine the value of the unknown side of a right triangle: The two legs of a right triangle are 5 ft and 12 ft. How long is the hypotenuse? Now Let the hypotenuse be c ft.
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Identify the flaw in the following argument which supposedly determines that n 2 is even when n is an even integer. As well name the reasoning: Assume that n 2 is
The base and corresponding altitude of a parallelogram are 10 cm and 12 cm reap. If the other altitude is 8 cm , find the length of the other pair of parallel side
Example Suppose the demand and cost functions are given by Q = 21 - 0.1P and C = 200 + 10Q Where, Q - Quantity sold
Q. Scaling and translation for equations? Ans. If you have an equation in the form y= f(x) (if you're not familiar with functions, that just means having "y" on the left s
2+(+3)=
1. A psychologist developed a test designed to help predict whether production-line workers in a large industry will perform satisfactorily. A test was administered to all new empl
Example Multiply 3x 5 + 4x 3 + 2x - 1 and x 4 + 2x 2 + 4. The product is given by 3x 5 . (x 4 + 2x 2 + 4) + 4x 3 . (x 4 + 2x 2 + 4) + 2x .
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