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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).
A right triangle whose sides are 15 cm and 20 cm is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Ans : 3768cu.cm,1318.8
Evaluate given integrals. ∫3/(5 y + 4) dy Solution Let's notice as well that if we take the denominator & differentiate it we get only a constant and th
If you have 60% alcohol and wish to dilute with water to make 12 liters 40% alcohol, How many liters of water should you add?
PLAY AND LEARN : Children can learn many basic mathematical concepts through games. They enjoy Mathematical concepts can be playing within familiar contexts. Their games also gen
If OA = OB = 14cm, ∠AOB=90 o , find the area of shaded region. (Ans:21cm 2 ) Ans: Area of the shaded region = Area of ? AOB - Area of Semi Circle = 1/2 x 14 x
Assume company A expects to enhance unit sales of i-phone by 15% per year for the next 5 years. If you presently sell 3 million i-phones in one year, how many phones do you expect
f(x)=sin(x),All x belongs to [p/6, p]
Find reference angle alpha and thea element of [0 degrees, 1800 degrees]
Graph y = tan ( x ). Solution In the case of tangent we need to be careful while plugging x's in since tangent doesn't present wherever cosine is zero (remember that tan x
Alexis needs to paint the four exterior walls of a large rectangular barn. the length of the barn is 80 feet the width is 50 feet and the height is 30 feet. The pain costs 28 dolla
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