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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).
We know that 2 4 = 16 and also that 2 is referred to as the base, 4 as the index or power or the exponent. The same if expressed in terms of logarithms would be log 2
ABC is a triangle right angled at c. let BC=a, CA=b, AB=c and lrt p be the length of the perpendicular from C on AB. prove that cp=ab and 1/p2=1/a2+1/b2
Can you explain that it is true that a line that slopes downward from left to right has a positive slope?
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The Fisher's index The index of Fisher acts as a compromise between Paasche' index and Laspeyre's index. This is calculated as a geometric mean of the two indexes.
Frequency Distribution or Variance Ratio Distribution This was developed by R. A Fisher in 1924 and is normally defined in terms of the ratio of the variances of two usually d
Relations in a Set: Let consider R be a relation from A to B. If B = A, then R is known as a relation in A. Thus relation in a set A is a subset of A ΧA. Identity Relation:
Area with Polar Coordinates In this part we are going to look at areas enclosed via polar curves. Note also that we said "enclosed by" in place of "under" as we usually have
What is Slope of a Line ? A line can have a "steep" slope or a "gradual" slope. slope = rise/run The "rise" is the distance going up or down. The "run" is the distance goin
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