Interpolate the value of the f(2,5) using Lagrange's interpolation formula with the following set of data. f(2)=5; f(3)=-1; f(4)=3; Take the precision as three digits by applying rounding methods. Write the answer below: P(2,5)=
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- Please construct the truth table of the following, thank you. a) [p→q] ꓥ [~p→q] b) [~p↔~q] ↔ [p↔q] c) [p→q] → [q→p] d) [pVq] ꚛ [pꓥq]Show using a truth table if the following statements are equivalent.a. ~(p ∨ q) and ~p ∧ ~qb. p → q and ~p ∨ qc. p ↔ q and [(p → q) ∧ (q → p)]d. p → (q ∨ r) and (p → q) ∨ (p → r)e. [p ↔ (q ∨ r)] ∨ q and (p → q) ∨ (p ↔ r)Build truth tables or abbreviated truth tables (on your own scratch paper) to determine whether the following arguments are valid or invalid. (A v B) --> (C • D), (X v ~Y) --> (~C • ~W), (X v Z) --> (A • E), ∴∴~X Group of answer choices A. Valid B. Invalid
- We initialize the parameters to all zero values and run the linear perceptron algorithm through these points in a particular order until convergence. The number of mistakes made on each point are shown in the table below. (These points correspond to the data point in the plot above) до Note: You should be able to arrive at the answer without programming. What is the resulting offset parameter 00? Enter the numerical value for 00: = 0 -1 -1 -1 -1 -1 +1 +1 +1 +1 +1 (0,0) (2,0) (3,0) (0,2) (2,2) (5,1) (5,2) (2,4) (4,4) (5,5) Perceptron mistakes 19 10 5 11 0 3 1 1 9 What is the resulting parameter ? (Enter as a vector, e.g. type [0,1] if = [01].) = Label Coordinates STANDARD NOTATIONUse the power series method to construct a polynomial interpolating (0,10),(1,18),(2,8),(3,−1) For both approaches, please construct the polynomials and plot the constructed polynomial interpolating the given data points. Please compare the polynomials from both approaches and see if they agree with each other. Require Python codeTwo trigonometric identities are given by: (sin x + cos x)2 = 1+ 2 sin x cos x 1- 2 cos x - 3cos2 x = 1- 3cos x sin2 x 1- cos x For each part, verify that the identity is correct by calculating the values of the left and right sides of the equation using MATLAT, substituting x=200 Find the solution to the systems + = ... .. . y + 3 y + 2 y y u Where y (0) =0; y’ (0) =0. u (t) is a square wave.
- 14) Draw the tableau for the following formula separately and check the satisfiability. ø= (p ¬q) s. ø= (t s) q ø= ¬ ((p q) r) ø= ¬ ((p q) p) 14) Draw the tableau for the following formula separately and check the satisfiability. ø= (p ¬q) s. ø= (t s) q ø= ¬ ((p q) r) ø= ¬ ((p q) p)Simplify the following expressions in normal form, if one exists: (λq. q q)(λs. s s a)Construct a truth table for ~[ (p ↔ q) ^ (r v ~p) ] → ~q. please use T or F.
- Construct a truth table for the statements belowa. (p ∧ q) ∧ (~r ∨ q).b. ~[~p ∧ (q ∧ r)]c. [p ∧ (q ∨ ~p)] → ~p then find the truth value of the statement givena. p is a false statement, q is a true statement and r is a true statement.b. p is a false statement, q is a false statement and r is a false statement.c. p is a false statement, q is a false statement and r is a true statement.draw a flow chart to accept n numbers and get the summation of negative, the summation of positive numbers and the count in each groupLet us design a Monte Carlo method to estimate the area of the shadow region under the green function y = ex when x is from 0 to r. As shown in the following figure, r is a variable (r> 0) for range. Please write a Python program named "A1Q1_MonteCarlo.py" to implement your designed Monte Carlo method. In the first line of your code, please write "n=10000" to define n as the experiment number of random sampling. Finally, please print out the estimated area for different range variables with the following format: When r=1, estimated shadow area is xxx When r=2, estimated shadow area is xxx When r=9, estimated shadow area is xxx When r=10, estimated shadow area is xxx [Hint]: You may need to use a loop for different range variables r and generate random sampling points automatically based on different range variables r.