Consider a set A = {a1, . . . , an} and a collection B1, B2, . . . , Bm of subsets of A (i. e., Bi ⊆ A for each i). We say that a set H ⊆ A is a hitting set for the collection B1, B2, . . . , Bm if H contains at least one element from each Bi – that is, if H ∩ Bi is not empty for each i (so H "hits" all the sets of Bi). We define the Hitting Set Problem as follows. We are given a set A = {a1, . . . , an}, a collection B1, B2, . . . , Bm of subsets of A, and an non-negative integer k. We are asked: is there a hitting set H ⊆ A for B1, B2, . . . , Bm so that the size of H is at most k? Prove that the Hitting Set problem is NP-complete

Write a program that displays the following menu: geometry calculator 1. calculate the area of a circle 2. calculate the area of a rectangle 3. calculate the area of a triangle 4. quit enter your choice (1-4): if the user enters 1, the program should ask for the radius of the circle and then display its area. use the following formula: area = ď€(the square of r) use 3.14159 for ď€ and the radius of the circle for r. if the user enters 2, the program should ask for the length and width of the rectangle and then display the rectangle’s area. use the following formula: area = length * width if the user enters 3, the program should ask for the length of the triangle’s base and its height, and then display its area. use the following formula: area = base * height * .5 if the user enters 4, the program should end. input validation: display an error message if the user enters a number outside the range of 1 through 4 when selecting an item from the menu. do not accept negative values for the circle’s radius, the rectangle’s length or width, or the triangle’s base or height. note: if the user enters an improper menu choice (1-4), the program prints "the valid choices are 1 through 4. run the program again and select one of those." if the user enters a negative radius, the program prints "the radius can not be less than zero." if the user enters a negative value for height or base, the program prints "only enter positive values for base and height."

Alcohol’s affects on the cornea and lens of the eye make it more difficult

A( the heart of an information system, is a collection of all relevant facts organized in a series of integrated files.