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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).
Mark is preparing a walkway around his inground pool. The pool is 20 by 40 ft and the walkway is intended to be 4 ft wide. Determine the area of the walkway? a. 224 ft 2 b.
Mona purchased one and a half pounds of turkey at the deli for $6.90. What did she pay per pound? Divide the cost of the turkey by the weight; $6.90 ÷ 1.5 = $4.60.
The value of K for (k+1)x^2-2(k-1)x+1 = 0 has real and equal roots.
There are really three various methods for doing such integral. Method 1: This method uses a trig formula as, ∫sin(x) cos(x) dx = ½ ∫sin(2x) dx = -(1/4) cos(2x) + c
How many relations are possible from a set A of 'm' elements to another set B of 'n' elements? Ans: A relation R from a set A to other set B is specified as any subset of A
How many permutations of the letters A B C D E F G H consist of string DEF? Ans: It is the dilemma of finding number of words that can be formed along with the given 8 lette
methods of interpolation
Example: A 16 lb object stretches a spring 8/9 ft by itself. Here is no damping as well as no external forces acting on the system. The spring is firstly displaced 6 inches upward
If roots of (x-p)(x-q) = c are a and b what will be the roots of (x-a)(x-b) = -c please explain. Solution) (x-p)(x-q)=c x2-(p+q)x-c=0 hence, a+b=p+q and a.b=pq-c
Which of the subsequent terms does NOT describe the number 9? Nine is NOT prime since it has 3 factors; 1, 3, and 9. Prime numbers have only 2 factors.
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