X is {a,b,c,d), Y is {1,2,3,4). {(a,1), (b,2), (c,2), (d,4)} is a function from X to Y.
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- Let A = {1, 2,3} and B = {a, b, c, d} What is the function from a to b?Q2) Simplify the following function for F using a K-map. F(A,B,C,D) = E m(0, 2, 8, 10, 12, 14)1. A set of integers are relatively prime to each other if there is no integer greater than 1 that divides all the elements. Furthermore, in Number Theory, it is known that the Euler function,ϕ (n), expresses the number of positive integers less than n that are relatively prime with n. Choose the alternative that has the correct value of ϕ(n) for every n below. A) ϕ(5) = 4 B) ϕ(6) = 2 C) ϕ(10) = 3 D) ϕ(14) = 6 E) ϕ(17) = 16
- [Unbalanced Rod] Given a set of n weights {w₁,..., wn} and a rod of length n - 1 inches, we can attach the weights to the rod at hooks placed at one inch distances apart as shown in the figure below. -1". /10 2 3 12 2 4 We can attach a weight to any hook but no two weights can be attached to the same hook and we have to attach all the weights. For any given assignment of weights to hooks, we can compute the location of the center of mass of the rod and the weights according to the following equation (neglecting the weights of the rod and the hooks). where 0 ≤ Pi≤n-1 is the position of weight along the rod. For example, in the figure shown above, the center of mass is computed as C= C = i Wi Pi Σi Wi 10 0+2 1+3·2+4·3+12.4 +2.5 10+2+3+4+12+2 78 33 The problem is to find an assignment of weights to hooks that makes the center of mass as far as possible to the left, i.e., minimize the value of c. Answer the following questions. 1. Describe a greedy algorithm that finds the assignments that…1. Reduce the following function: ((A O B)•(A•C) )•( (A•B) +(A © B) )Q1: Y=f{A,B,C.D,E.F)=Em (0,1,2,4,5,6,7,9,13,15,17,19,21,23,26,27,30,31,33,37,39,40,42,44,45,4 6,47,49,53,55,57,59,60,61,62,63) Design the function with minimal logic gates and simplify the functions Using Karnaugh Map Method.
- 5. Simplify the following functions using a K-map: e)F(X,Y,Z)=X'Y'Z'+X'YZ+XY'Z+XYZ5. Simplify the following functions using a K-map: c)F(X,Y)=X'+XY'True or False 1. Matrices are often represented by single small letters a, b, c... etc.2. Two m x n matrices A and B are equal if aij=bij for each i & j. (i.e., the two matrices havesame size, and all the corresponding elements are equal).3. Matrices A & B are said to be conformable in the order AB if, and only if, the number ofrows in A is equal to the number of columns in B.4. Suppose Matrix A is having 4 rows and 3 columns, and Matrix B is having 3 rows and 2columns. The product size of AB is a 4 x 2 matrix.5. Suppose B is the matrix obtained from an n x n matrix A by multiplying the entries in arow/column by a non-zero constant and adding the result to the corresponding entries inanother row/column. Then, det(B) = det(A).