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- Ql: The Collatz conjecture function is defined for a positive integer m as follows. (COO1) g(m) = 3m+1 if m is odd = m/2 if m is even =1 if m=1 The repeated application of the Collatz conjecture function, as follows: g(n), g(g(n)), g(g(g(n))), ... e.g. If m=17, the sequence is 1. g(17) = 52 2. g(52) = 26 3. g(26) = 13 4. g(13) = 40 5. g(40) = 20 6. g(20) = 10 7. g(10) = 5 8. g(5) = 16 9. g(16) = 8 10. g(8) = 4 11. g(4) = 2 12. g(2) = 1 Thus if m=17, apply the function 12 times in order to reach m=1. Use Recursive Function.arrow_forwardFor all a and b in the domain of a function f, the function is injective iff f(a) #f(b) a=Db f(a)=f(b) a=b f(a)=f(b) atb o fly)=x iff f(x)=y A Moving to another question will save this response. 5arrow_forwardH.W2 Minimize the following function using K-Maps: F (A, B, C, D) = Σ m (1, 5, 6, 12, 13, 14) + d (2, 4).arrow_forward
- In a company, there are several branches. Let us consider a branch of that company having N employees, if the manager is allotted to that branch(s) then he is known to everyone else in that branch. Note that the property of "known to everyone" is unique to a manager. Your task is to find the manager in that branch. Input from the user in main (), the square matrix M where if an element of row i and column j is set to 1 it means that ith person knows jth person. You need to write a function managerId () which returns the id of the manager if present or else returns -1. The function managerId () takes two arguments - the square matrix of N *N and its size N. Call managerId () from the main () output the information about the manager. Assume all diagonal elements to be 1 (as everyone knows him/herself) and there is at most one manager in the company.arrow_forward5. Simplify the following functions using a K-map:(a) F(X,Y)¼m2+ m3arrow_forwardCreate K-maps and then simplify for the following functions. 3) F(x, y, z) = xyz + xy’z’ + x’yz + x’y’zarrow_forward
- Q. Let A = {a, b, c, d, e} and B = {1, 2, 3, 4, 5, 6, 7, 8}. How many functions f : A → B(a) ... are injective?(b) ... are not injective?(c) ... are such that f(a) = f(b) = f(c)?(d) ... are such that exactly three elements of A have 8 as an image?(e) ... are surjective?arrow_forwardLet A = {1, 2,3} and B = {a, b, c, d} What is the function from a to b?arrow_forward8. X. Let f: RR defined by f(x) = x³ -arrow_forward
- 2. Definition: If f(x) is a function, then we say that a value u is a fixed point of f(x) if and only if f (u) = u. Suppose F(x) is a given continuous function and a # 0 is a given real number. Show that u is a zero of F(x) if and only if u is a fixed point of f (x) f (x) = x + a F (x). b. Suppose F '(x) is continuous, u is a zero of F, and F'(u) ± 0. Define f (x) = x + aF(x). Prove there are values of a + 0 and ɛ > 0 so that if uo E (u – E, u + ɛ) and un+1 = f (Un) for n = Hint: Jun+1 – u| = \f (un) – f (u)]. Use the definition of f (x) and the mean а. = 0,1,2, ... then un → u as n → ∞. | value theorem.arrow_forward3. (a) Consider the following algorithm. Input: Integers n and a such that n 20 and a > 1. (1) If 0arrow_forwardDetermine whether each of the following functions f : {a,b,c,d} -> {a,b,c,d} is one-to-one and/or onto. (a) f(a) = b, f(b) = a, f(c) = b, f(d) = c (b) f(a) = b, f(b) = b, f(c) = d, f(d) = c (c) f(a) = b, f(b) = a, f(c) = c, f(d) = d (d) f(a) = d, f(b) = a, f(c) = c, f(d) = b (e) f(a) = c, f(b) = d, f(c) = aarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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