Simplify (pv(mA-p)) to p^-m 1. Select a law from the right to apply -(pv(m^-p))
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- Define a sequence c0, c1, c2, … of pictures recursively as follows:For all integers i ≥ 1 Initial Conditions, c0 = an upright equilateral triangle ?. Recurrence Relation, ci = in centre of each upright equilateral triangle in ci-1, draw an upside down equilateral triangle ? such that its corners touch the edges of the upright one. Draw the first 4 iterations, starting with c0. You may want to draw c3 large. Each should be a separate drawing.Get your work checked by an IA/TA/Instructor. Count the total # of triangles for each iteration in a).Note: Triangles can be of any orientation.Only count the individual triangles. Do not count a triangle which has triangles inside it. Determine T(0), the # of triangles in the 0th term. Determine the recurrence relation, T(n), that gives the # of triangles in the nth term, for n ≥ 1.Show that the relation R consisting of all pairs (x, y) suchthat x and y are bit strings of length three or more thatagree except perhaps in their first three bits is an equivalence relation on the set of all bit strings of length threeor more.5 Consider the degree-4 LFSR given by x to the power of 4 space plus space x squared space plus space x space plus space 1. Assume that the LFSR is initialized with the string left parenthesis s subscript 0 s subscript 1 s subscript 2 s subscript 3 right parenthesis equals left parenthesis 0110 right parenthesis. How long is the cycle generated?
- What is the time and space complexity of this function? It is a dfs function which goes through every possible path from node to another without cycles. Time complexity could be either O(n!) or O(2^n), or is there another answer? What is the space complexity? def dfs(currency_pairs, source, target): graph = defaultdict(dict) for s1, s2, rate_val1, rate_val2 in currency_pairs: graph[s1][s2] = rate_val1 graph[s2][s1] = rate_val2 def backtrack(current, seen): if current == target: return 1 product = 0 if currentingraph: neighbors = graph[current] for neighbor in neighbors: if neighbor not in seen: seen.add(neighbor) product = max(product, graph[current][neighbor] * backtrack(neighbor, seen)) seen.remove(neighbor) return product return backtrack(source,…Suppose (X[mX]+Y [mY ]) > 0. What can you infer about each of the four subproblems (namely, (X1, Y1), (X1, Y2), (X2, Y1), and (X2, Y2))? Clearly identify the ones that do not have to solved anymore, and those that still have to be solved. Briefly justify.give an example of a network with no more than 6 nodes and define all the data structure used by a distence vector and a link state algorithm. perform one iteration for both the algorithm families and show the aforementioned structires are uptaded
- A star configuration of a network represents its structure as a graph with an edge from a single, central node to each remaining node. A point-to-point configuration represents a network as a complete graph. Draw a picture of an example of each kind of configuration with four nodes, and use big-O notation to state the efficiency of adding or removing a given node in each type of configuration. You can assume for now that removing each edge is a constant-time operation. *PythonHow many double precision values would be required to generate a finite difference approximation for a real world domain that has 101 nodes in x, 41 nodes in y, and 41 nodes in z. Do not forget the right hand side vector b, but do not include the solution vector x. How much memory in Gb would be required for A and b assuming a double requires 8 bytes (round up to the nearest mb)solve the following questions Q1Let the string having length eight of an arrays is defined as ; 01001010 ii. 01101101 Apply the definition of propositional logic conjunction and disjunction on it. Q2 a). Define pandent vertex and isolated vertex by giving example. (b). Show that “¬ p v q” is logically equivalent to “pq”. Q3 a). Consider the propositional function (,) defined by ; What is the truth value of (-2,4,-5)? What is the truth value of (6-,2,8)? (b). Write down the difference between universal quantifier and existential quantifier by giving examples. Q4 Let ‘H’ and ‘G‘ are two non-empty sets which are defined as; and modulus function defined by; Check the defined absolute value function for injective. Q5 Given a simple graph “N” as below in figure ; graph is attached below Check it for the following ; Find chromatic…
- In reference to deep learning, can a multilayer perceptron of width (n+1) calculate any function from Rn to R ?Can you explain this? What are the correct explanations for pooling layers? (Multiple Answers Possible) A. An average pooling layer is differentiable since it is a linear operation. B. A max pooling layer has strictly fewer learnable parameters than a convolutional layer. C. A max pooling layer can be used between convolutional layers without breaking the computation graph. D. A pooling layer must include a non-linear activation function.Reduce the proposition using laws Simplify q∨(w∧¬w) to q Select a law from below to apply to: q∨(w∧¬w) Laws Distributive (a∧b)∨(a∧c)≡a∧(b∨c) (a∨b)∧(a∨c)≡a∨(b∧c) Commutative a∨b≡b∨a a∧b≡b∧a Complement a∨¬a≡T a∧¬a≡F Identity a∧T≡a a∨F≡a Double negation ¬¬a≡a