Assume that in a group of six people, each pair of individuals consists of two friends or two enemies. Show that there are either three mutual friends or three mutual enemies in the group.

Let’s consider a long, quiet country road with houses scattered very sparsely along it. (We can picture the road as a long line segment, with an eastern endpoint and a western endpoint.) Further, let’s suppose that despite the bucolic setting, the residents of all these houses are avid cell phone users. You want to place cell phone base stations at certain points along the road, so that every house is within four miles of one of the base stations. Give an efficient algorithm that achieves this goal, using as few base stations as possible.   Give the psudo code.

Consider the following scenario:A high school has 1000 students and 1000 lockers, one locker for each student. On the first day of school, the principal plays the following game: She asks the first student to open all the lockers. She then asks the second student to close all the even-numbered lockers. The third student is asked to check every third locker. If it is open, the student closes it; if it is closed, thestudent opens it. The fourth student is asked to check every fourth locker. If it is open, the student closes it; if it is closed, the student opens it. The remaining students continue this game. In general, the nth student checks every nth locker. If it is open, the student closes it; if it is closed, the student opens it. After all the students have taken turns, some of the lockers are open and some are closed. The program see in the photo, when ran, should ask the user to enter the number of lockers in the school. The program will output the number of lockers and the…

For (∃ x)(P(x,b)) Would an example of this being true if the domain was all the Avengers and x was green skin, then "b" being the Hulk would make this true. Am example of this being false would be: If the domain was all integers and x was positive, even integers and "b" was integers greater than zero.

Four individuals wish to traverse an unstable bridge; they all start on the same side. You have 17 minutes to get everyone to the opposite side. Night has fallen, and they have only one torch. Two individuals may cross the bridge at once at most. Any crossing party, whether one or two individuals, must carry a torch. The torch must be carried back and forth; it cannot, for instance, be hurled. Person 1 crosses the bridge in one minute, person 2 in two minutes, person 3 in five minutes, and person 4 in ten minutes. A dyad must trek together at the slower individual's cadence. Create the algorithm specification that solves the problem.

Please do the exercise thank youuu

A publisher plans to boost the sales of its most popular magazine by sending out promotional mails. We refer to a customer as a responder if he/she subscribes to the magazine for the next year after receiving a promotional mail. Otherwise the customer is referred to as a non-responder. Denote responder by C1 and non-responder by C2. The publisher has built a model to classify each customer as either a responder or a non-responder. In practice only 1% of the customers are responders, and the remaining 99% are non-responders. In order to build an unbiased model, the publisher employed the oversampling method in creating the training set and the validation set, such that both datasets contain 50% responders and 50% non-responders. The validation confusion matrix is given below.   Actual Class C1 C2 Predicted Class C1 645 112 C2 255 788   Round your answers to 3 digits after the decimal point. The oversampling factor of C1 is  . The oversampling factor of…

You have a backpack that can carry at most 15 kg of stuff (following image). There are ten boxes of five types (A, B, C, D, and E), with two boxes of each type. The weights and values of the boxes are given in the figure. You want to select some of these boxes to put in your backpack in order to maximize their total value, but you cannot exceed the backpack’s weight capacity. Additionally,• if a type B box is selected, then no type C box can be selected• at least one box of either type A or type D must be selected Formulate an integer linear programming model to help you make the bag packing decision. To assist you, below are your decision variables.• yi: select (= 1) or not select (= 0) type i box, i = A, B, C, D, E.• xj: The number of type j boxes selected, j = A, B, C, D, E.