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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
A vessel in shape of a inverted cone is surmounted by a cylinder has a common radius of 7cm this was filled with liquid till it covered one third the height of the cylinder. If the
a pair of straight lines are drawn through the origin forms with the line 2x+3y=6 an isoceles triangle right angled at origin find the equation of pair of straight line?
A parcel of land, value $250,000 is sold to an investor who signs a contract agreeing to pay a deposit of $25,000 followed by equal quarterly payments for as long as necessary, wit
Probability - Applications of integrals In this final application of integrals that we'll be looking at we are going to look at probability. Previous to actually getting into
Write an algebraic expression for “Julie runs three miles less than twice the number of miles,
) Show that the following argument is valid: (~p ? q) => r s ? ~q ~t p => t (~p ? r) => ~s ------------------------ ? ~q 2) Show that the following argum
Write down the first few terms of each of the subsequent sequences. 1. {n+1 / n 2 } ∞ n=1 2. {(-1)n+1 / 2n} ∞ n=0 3. {bn} ∞ n=1, where bn = nth digit of ? So
Apply depth-first-search to find out the spanning tree for the subsequent graph with vertex d as the starting vertex. Ans: Let us begin with node'd'. Mark d as vi
A number of the form x + iy, where x and y are real and natural numbers and is called as a complex number. It is normally given by z. i.e. z = x + iy, x is called as the real part
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