Week Five Final Exam Instructions: Complete the following exercises below. Partial credit will be awarded as long as the reasoning used to arrive at the solution is provided. The point value of each problem is given in parentheses for a maximum of 50 points. 1) (8 pts) Suppose we are given the following expression: (x + xy) + (x/y). Represent this expression as a binary tree. 2) (10 pts) Use the rooted tree below to perform a pre - order traversal of the expression. 3) (6 pts) Determine whether the relation R on the set of all people is reflexive, symmetric, anti- symmetric, and/or transitive, where (a, b) ϵ R if and only if a is taller than b. 4) (8 pts) Find the dual of the following Boolean expression. 5) (10 pts) Use a table to express the values of the Boolean function. F(x, y) = 6) (8 pts) Find the output of the given circuit.

I don't need it till end of the week, but if you can get it done asap so i can turn it in would be greatly appericate it. Also if you can show your work and or explain your answer would also be awesome