Find witnesses to show that f(x) = 7x^4 − 5x^2( + 2 is Θ(x^4);
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Find witnesses to show that f(x) = 7x^4 − 5x^2( + 2 is Θ(x^4);
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- 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?Prove by Systematic Semantic Tableaux ∃xR(x,x)∨∃x[R(x,x)→¬∃yR(y,x)]Show validity by natural deduction: ∀x[p(x) → q(x)] → [(∃xp(x) ∧ ∃xr(x)) → ∃xq(x)]
- Show that (p ∧ q) → r and (p → r) ∧ (q → r) are not logically equivalent, without using truth tables.(a) Given a DFA M = (Q, Σ, δ, q0, F), consider M' = (Q, Σ, δ, q0, F'), where F' = Q − F. Prove that L(M') is the complement of L(M). (b) Give a counter-example to show that the above construction with NFAs does not (always) yield the complement.Graph the functions 8n, 4nlogn, 2n2, n3, and 2n using a logarithmic scale for the x- and y-axes. That is, if the function is f(n) is y, plot this as a point with x-coordinate at log n and y-coordinate at log y.
- Simplify the following Boolean expressions, using four-variable maps: (a) A'B'C'D' + AC'D' + B'CD' + A'BCD + BC'D (b) x'z + w'xy' + w(x'y + xy') (c) A'B'C'D + AB'D + A'BC' + ABCD + AB'CPlease help me make a Truth Table on this F = A'B'C' + A'BC + AB'C + ABC' + ABC please make like this in my example attached photo.Construct a truth table for each proposition. a.) [(p ∧ q) ∨ r ] ↔ [(p ∧ r ) ∨ (q ∧ r )] b.) [(p ∧ r ) → (q ∧ ¬r )] → [(p ∧ q) ∨ r )]
- Consider the following confusion matrix for 5 variables Predicted A’ B’ C’ D’ E’ ActualA 25 5 2 10 7B 3 32 4 16 2C 1 0 15 4 6D 3 6 1 40 12E 40 32 12 1 98 Calculate Precision, Recall, F-Measure and Accuracy for Class A and Class DBy filling out a truth table, show that r ∧(q →p)→r→(q∧p)and ¬r∨q are logically equivalent.Please explain how to complete this truth table. If W is greater than X, then A is 1, B and C are 0. If W is equal to X, then B is 1, A and C are 0. If W is less then X, then C is 1, A and B are 0.