I am not sure about the graph which graph you want to show the whole relationship among X, Y and Z. I am using here venn diagram(It is aslo a graph) to show the relationship.
There are two cases arise to map the problem here:-
Case 1. when Z knows 5 students in class.

Case 2. When Z knows 3 students in class.

If you are exxpecting some other graph, you can ignore the solution. Thank you.
"A class has 8 students. Suppose that three students X, Y and Z do not know...
4) A class has 8 students. Suppose that three students X, Y and Z do not know each other. X knows 4 students of the class, Y knows 3 students of the class. At least how many students must Z know to make sure that always there is one student that knows X, Y, and Z? (Explain by using a graph to model the relationships).
Problem 3 (3pts) ment "x is a class", let S(x) be the statement " x is a student" and let I(x,y) be the statement "x is in y". Translate the followings into formulas. Let P(x) be the statement "x knows functional programming", let C(x) be the state- Every class has a student who knows functional programming. Every student in every class knows functional programming. There is at least one class with no students who know functional programming. Problem 4 (2pts)...
3. Suppose my graph theory class has 12 different students, of which 6 are under- grads and 6 are graduate students. (a). How many ways can I choose at least 4 but no more than 8 of my students to take a field trip to the library? (b). I want to repeat part (a), but I want to be sure to take at least 2 undergrads. (c). I have 3 different final projects for them to work on (projects A,...
Suppose three random variables X, Y, Z have a joint distribution PX,Y,Z(x,y,z)=PX(x)PZ∣X(z∣x)PY∣Z(y∣z). Then X and Y are independent given Z? True or False Suppose random variables X and Y are independent given Z , then the joint distribution must be of the form PX,Y,Z(x,y,z)=h(x,z)g(y,z), where h,g are some functions? True or false
3. Suppose you and your class mate have to do a group assignment. Both of you can decide to work or shirk. If you both work, then both will get a good mark but both incur the cost of working. If one person works, you get a bad mark but the person who shirked will not have to put in the effort. If both shirk then the students fail. The following table represents the individuals’ utilities (as always the first...
Suppose the average age (mean) for students in the class is 21 years. What do we know about the distribution of students' ages for this class (e.g., Are they all about 21 years old?)? Explain. Where does that number (21) come from? Explain.
Suppose that the assumptions of the Standard Trade Model apply. Consider three countries: X, Y and Z. Consider two goods: A and B. X and Y export A and import B. Z exports B and imports A. Moreover, suppose that country Y (which is a large country) experiences economic growth in its import sector. Explain in detail, using any relevant diagrams, what is the effect of this growth on the welfare of Z?
Suppose that the assumptions of the Standard Trade Model apply. Consider three countries: X, Y and Z. Consider two goods: A and B. X and Y export A and import B. Z exports B and imports A. Moreover, suppose that country Y (which is a large country) experiences economic growth in its import sector. Explain in detail, using any relevant diagrams, what is the effect of this growth on the welfare of (a) X?
Suppose that the assumptions of the Standard Trade Model apply. Consider three countries: X, Y and Z. Consider two goods: A and B. X and Y export A and import B. Z exports B and imports A. Moreover, suppose that country Y (which is a large country) experiences economic growth in its import sector. Explain in detail, using any relevant diagrams, what is the effect of this growth on the welfare of X
Suppose that the assumptions of the Standard Trade Model apply. Consider three countries: X, Y and Z. Consider two goods: A and B. X and Y export A and import B. Z exports B and imports A. Moreover, suppose that country Y (which is a large country) experiences economic growth in its import sector. Explain in detail, using any relevant diagrams, what is the effect of this growth on the welfare of X