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- Given A = {1,2,3} and B={u,v}, determine. a. A X B b. B X Barrow_forward(V, E) be a connected, undirected graph. Let A = V, B = V, and f(u) = neighbours of u. Select all that are true. Let G = a) f: AB is not a function Ob) f: A B is a function but we cannot always apply the Pigeonhole Principle with this A, B Odf: A B is a function but we cannot always apply the extended Pigeonhole Principle with this A, B d) none of the abovearrow_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_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_forwardQ. 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_forwardThe function of four variables G (A, B, C, D) = Z (2, 3, 8, 9, 11, 14, 15) + F (6, 10) is given. Here F values are "Doesn't matter" (Indeterminate) values that can take any value. Write this function in a simplified form using the Karnaugh Map.arrow_forward
- Let 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_forward2. 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_forward
- d) for (k0; k=0; t = t-1) printf("B"); for-t: TC1iter) = Change of var: Σ/repetitions, Closed form: for-k: TC1iter) =. Change of var: Σ/repetitions Closed form: dependent / independent of loop variable dependent / independent of loop variable e(arrow_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_forward8. Define a function polyMult p q that returns the product of p and q. For example: poly Mult [(3.0,2), (2.0,1), (1.0,0)] [(3.0,1), (2.0,0)] should evaluate to [(2.0,0), (7.0,1), (12.0,2), (9.0,3)] (or equivalent). Use the fact that when n > 0, ao+a₁×x+a2×x²+...+anxx" is expressible as a0+xx(a₁x+a2××+ ··· +an×xn−1) and thus provide a recursive definition that uses polynomial addition (implemented earlier) and а тар.arrow_forward
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