Mathematics Questions -

Q1. Consider the following directed graph.

Give the outdegree of each vertex.

Q2. Consider the following directed graph.

Compute sum of the indegrees and the sum of the outdegrees.

What do you notice?

The sum of the indegrees is one more than the sum of the outdegrees.

The sum of the indegrees and the sum of the outdegrees are not equal, but they are multiples of each other.

The sum of the indegrees equals the sum of the outdegrees.

The sum of the outdegrees equals twice the sum of the indegrees plus 1.

The sum of the outdegrees is one more than the sum of the indegrees.

Q3. Consider the following directed graph.

Give the indegree of each vertex.

Q4. Consider the following list of numbers.

129, 689, 125, 515, 604, 54, 47

Place the numbers, in the order given, into a binary search tree.

Q5. Place the following words in a binary search tree. Add the words to the tree in the order given.

Lame, good, great, super, worthwhile, excellent, poor

Q6. In a class of 60 students, everyone has either a pierced nose or a pierced ear. The professor asks everyone with a pierced nose to raise his or her hand. Nine hands go up. Then the professor asked everyone with a pierced ear to do likewise. This time there are53 hands raised. How many students have piercings both on their ears and their noses?

Q7. Let the following sets be given. The universal set for this problem is the set of all students at some university.

F = the set of all freshmen

S = the set of all seniors

M = the set of all math majors

C = the set of all CS majors

Using only the symbols F, S, M, C, ||, ∩, ∪, ', and >, translate the following statement into the language of set theory.

There are more freshmen who aren't math majors than there are senior CS majors.

Q8. Write down all elements of ({6, 7, 8} ∩ {7, 8, 9, 10}) ∪ {11, 12}. (Enter your answer in set notation.)

Q9. An integer solution to the equation 3x + 4 = 7y, is an ordered pair of integers (x, y) that satisfies the equation. For example, (1, 1) is one such solution. Write the set of all integer solutions to the equation 3x + 4 = 7y in set builder notation.

Q10. Consider the following list of numbers.

127, 681, 124, 516, 602, 51, 44

The height of a binary search tree is the maximum number of edges you have to go through to reach the bottom of the tree, starting at the root. What is the height of the tree for the numbers above, in the order given?