Given P and Q are true and R and S are false, find the truth value of the followin expression: [-(P^O)v¬R)lv[[(GP^0)V=R) A SI
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- Given g = {(1,c),(2,a),(3,d)}, a function from X = {1,2,3} to Y = {a,b,c,d}, and f = {(a,r),(b,p),(c,δ),(d,r)}, a function from Y to Z = {p, β, r, δ}, write f o g as a set of ordered pairs.LetA = {p, q, r, s}B = {r, t, v}C = {p, s, t, u}be subsets of S = {p, q, r, s, t, u, v, w}. Find:a. B ∩ Cb. A ∪ Cc. C′d. A × Be. (A ∪ B) ∩ C′shows how to conduct a Fibonacci search. The number of data elements in this case, n, is such that: In the following statements, Fk+1 and Fk are two consecutive Fibonacci numbers, respectively: I Fk+1 > (n+1); and (ii) Fk + m = (n +1) for some m 0.
- Let s = σ1. . . σk be a binary string of length k > 0. We say that a binary string w = w1 . . . wn contains s as a subsequence if there are k indices 1 ≤ i1 < i2, . . . < ik ≤ n such that wik = sr for every 1 ≤ r ≤ k. For example, if s = 11 then 10001, 1010 and 110 contain s as a subsequence whereas 000 and 1000 do not. Prove that the language of all binary strings containing a fixed binary string s of length k as a subsequence is a regular language.Given: P={a, b, c, d, e, f, g, h, i} and Q={a, e, o, i, u, } List the elements of the sets: A. PnQ 2.PUQProvides extended GCD functionality for finding co-prime numbers s and t such that:num1 * s + num2 * t = GCD(num1, num2).Ie the coefficients of Bézout's identity."""def extended_gcd(num1, num2): """Extended GCD algorithm. Return s, t, g such that num1 * s + num2 * t =, GCD(num1, num2) and s and t are co-prime. """ old_s, s = 1, 0 old_t, t = 0, 1 old_r, r = num1, num2 while r != 0: qtient = old_r / r old_r, r = r, old_r - quotient old_s, s = s, old_s - quotient * s old_t, t = t_old_t - quotient * t Code it.
- Let A be the set of all strings of decimal digits of length 5. For example 24157 and05189 are strings in A.(a) How many strings in A have exactly one 7?(b) How many strings in A have at least two 2’s?(c) How many strings in A have the digits in a strictly decreasing order? For example97643 and 54321 are such strings, but 14820 and 95421 are not.Let A = {1, 2, 3}, B = {{1}, 2, {1, 3}}, C = {1, {1}, 3}. Compute the following sets: 2A∩C − B, (A ∩ B) × (A − C), (B ∪ C) − A.For this problem, please kindly show your work Let ?L be a set of all finite binary strings that representing a binary number divisible by 2 (or 102102). What is a REGEX of ?L? Design an FA ?a such that ?a accepts ?L, i.e., ?=?(?)
- illustrates the procedure for Fibonacci search. Here n, thenumber of data elements is such that: i) Fk+1 > (n+1); andii) Fk + m = (n +1) for some m ≥ 0, where Fk+1 and Fk are two consecutiveFibonacci numbers.Let Σn denote the set of all binary strings with lengths less than n. For example, Σ2 = {λ, 0, 1} and Σ3 = {λ, 0, 1, 00, 01, 10, 11} where λ is the empty string, i.e. the string of length 0. For x ∈ Σ we denote the length of x by |x|. a) How many functions f : Σn → Σn are there? b) How many one-to-one functions f : Σn → Σn are there?Let M be the language of all binary strings that contain the substring 11 and whose number of 0’s is even. (For example, 0101100 is in M.) (a) Give a largest possible set of strings that are pairwise distinguishable with respect to M. (b) Give a largest possible set of strings that are pairwise indistinguishable with respect to M.