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- Use the following definitions to express each union or intersection given. You can use roster or set builder notation in your responses, put no set operations. For each definition, i e Z* • A; = {i°, i', i²} (Recall that for any number æ, xº = 1.) • B; = {x € R : -i < x <1/i} • C; = {x €R: -1/i < x <1/i}(Prove using Direct Proof)Theorem: Directly prove that if n is an odd integer then n^2 is also an odd integer.Proof:(10111100)ex-3 = ( )10 O a.-60 O b. 188 O c. 98 Od. 89
- - (Difficulty: *) Consider the sequences x1 [n] = cos(2rn· /2/30) 22[n] = cos(2rn - 1.41421356/30) with n E Z Select the correct statements below. There exists N E N for which x2[n] has a DFS of size N There exists N E N for which a1 [n] has a DFS of size NTo correct the following code syms y(t); dsolve(diff(y,t)=2*t); * there is no error in the code = should be replaced by == None of the choices Replacing diff(y,t) by diff(y) will solve the issue1. (25.375), = (?.?), %3D 2. True error is defined as 3. The relative approximate error at the end of an iteration to find the root of an equation is 0.004%. The least number of significant digits we can trust in the solution is 4. The number 0.01850x10 has significant digits 5. The number of significant digits in the number 219900 is
- ii. find the value of N so that y less than 0.00000075.137 (base 10) = (base 4) (use subtraction method) Your Answer:To correct the following code syms y(t); dsolve(diff(y,t)=2*t); * Replacing diff(y,t) by diff(y) will solve the issue there is no error in the code = should be replaced by == %3D None of the choices
- identify 8 Errors in the following code give a reason why .Please do not give the same answer, need a different code6.Coding-----""Euler's totient function, also known as phi-function ϕ(n),counts the number of integers between 1 and n inclusive,which are coprime to n.(Two numbers are coprime if their greatest common divisor (GCD) equals 1)."""def euler_totient(n): """Euler's totient function or Phi function. Time Complexity: O(sqrt(n)).""" result = n for i in range(2, int(n ** 0.5) + 1): if n % i == 0: while n % i == 0: n //= i.