1. Create one Binary Search Tree and delete nodes from it. Specifically, you have to draw diagrammatically the trees that appear from the following (just the final form): a) Draw the Binary Search Tree using the following data entered(once) in this order:27,59,21,38,54,63,8,70,15 b) Draw the Binary Search Tree which appears if the value 59 is deleted from the Binary Search Tree you drew in 1a. c)Draw the Binary Search Tree which appears if the root of the Binary Search Tree you drew in 1a is deleted.

4. Prove by direct proof that "“The square of an even integer is even" uith .uithaut

What is the answer for z by 8? that answers missing

Long chain of friends: You are given a list of people, and statements of the form “x knows y”. You are asked to find, is there a chain of k distinct people, such as x1 knows x2, x2 knows x3, and xk-1 knows xk. Prove that this problem is NP-complete by using one of the known NP-complete problems (CLIQUE, 3-SAT, Hamiltonian Path, Hamiltonian Cycle, Independent Set, etc.)

Find the value of x for the following sets of congruence using the Chinese remainder theorem.a. x ≡ 2 mod 7, and x ≡ 3 mod 9b. x ≡ 4 mod 5, and x ≡ 10 mod 11c. x ≡ 7 mod 13, and x ≡ 11 mod 12

Prove each statement using a proof by exhaustion.

In this group of problems, you are given the predicate P(x), where the domain of x is the set of natural numbers.

please answer and circle the final answer. I dont understand how to do this please help!

Show that StartFraction d Over dx EndFraction ​(ln kx​)equalsStartFraction d Over dx EndFraction ln x​, given that xgreater than 0 and kgreater than 0 is a real number.

Solve and show each step using the Master Method Theorem.