(proof by contraposition) If the product of two integers is not divisible by an integer n, then neither integer is divisible by n
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(proof by contraposition) If the product of two integers is not divisible by an integer n, then neither integer is divisible by n
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- (Prove using Direct Proof)Theorem: Directly prove that if n is an odd integer then n^2 is also an odd integer.Proof:(True or False) Seven different positive integers are randomly chosen between 1 and 2022 (including 1 and 2022).There must be a pair of these integers has a difference that is a multiple of 6.4) / Using contraposition, prove that if 3n+4 is even, then n is even, where n is an integer.
- 2. If n is a positive integer, then n4 - n is divisible by 4. [Proof of Exhaustion](100 N3+N and 10 N) has a Big-Oh of N. Choose one: Is it true or false?(ABET 2) Construct a regular expression corresponding to the following set: {binary strings such that every odd position is a 1}. You may assume that the even positions can be a 0 or 1.
- Q1) Write a computer program that uses Newton's method to find the root of a given function, and apply this program to find the root of the following functions, using co as given. Stop the iteration when the error as estimated by n+1 - Enl is less than 10-6. Compare to your results for bisection. (a) f(x) = 1-2xe-/2, xo = 0; (b) f(x)=5-x-¹, x = ¹; (c) f(x)= x³ - 2x - 5, xo = 2; (d) f(x)=e-2, xo = 1; (e) f(x)=x-e, xo = 1; (f) f(x)=x-x-1, xo = 1; (g) f(x)=x²-sinx, xo =/; (h) f(x)= x³-2,0 = 1; (i) f(x) = x + tan x, zo = 3; (j) f(x)=2x-¹ In x, xo = 3.Write all permutation for ABC. (Consider as a letter A, B,C).(in python)(01+011+0111)* create a non-deterministic automaton of the above expression