A league of 20 teams is playing a "round-robin" style tournament, where each team plays every other team exactly once. How many games total need to be played? _____ Justify your...

A league of 20 teams is playing a "round-robin" style tournament, where each team plays every other team exactly once. How many games total need to be played? _____ Justify your...

Definition. An integer n is alphic if n = 4k + 1 for some integer k. Definition. An integer n is gammic if n = 4k + 3 for some integer k. Show that 19 is gammic. 19 = 4 ( ___...

In a class of 30 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. Seven hands go up. Then the professor asked...

128, 682, 121, 516, 601, 51, 49 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...

(Enter your answer in set notation.)

what is the truth value of the following

I need to express my result as a polynomial, we were given formulas which states the answers however I cannot find the formulas for these last 2 A) C(n+2,n) C) C(C(n,k),(n¦(n-k)))...

Suppose that R is a ring of characteristic n. If addition and multiplication are defined in R x Zn = {(x, a)lx E R; a E Zn} by (x, a) + (y, b) = (x + y, a +n b), (x, a)(y, b)...

Hi I have 2 problems that I need to say whether or not they are true or not and then write a proof for my answer. I am really struggling and could use a little help thank you 1) ...

1. How many different positive integers can be made from the digits {2, 4, 6, 8} if repetitions are allowed? 2. What is the telescoping form of f(x) = x4 + 7x3 - x2 + 2x +...

prove it if it is correct or give counterexample if it is false let d=(a,b) then a|bc if and only if a/d is a divisor of c

Can anyone tell me if: F(n) = 3n^2 + 1 is one-to-one or onto? I'm pretty sure it's neither because n^2 itself isn't onto, but I need second opinions...

Here are four relations defined on R, the set of real numbers: R1 = { (x, y): x ≤ y } R2 = { (x, y): x > y } R3 = { (x, y): x < y } R4 = { (x, y): x = y } Describe...

The Fibonacci sequence F0, F1, F2, F3, ... is an infinite sequence defined by the two initial values F0 =0, F1 =1, and the rule Fk = Fk-2 + Fk-1 for all k ≥ 2. Let Μ...

There are 57 students in a class, how many different ways can you make a group of 5?

f(x) = -(x - 1) g(x) = 2x2 h(x) = 3x + 1 a. What is (f ο g)(-2)? b. What is (g ο f)(-2)? c. What is (f ο h)-1(3)? d. What is (f ο g ο h)(1)? e. What is (h ο h-1)(π)...

Consider the surjective function cos: R → [−1, 1] and let ∼ be the associated equivalence relation x ∼ y ⇐⇒ cos x = cos y. Describe the equivalence classes of ∼...

please I want help with that Consider the ring Mn(R) ofn x n matrices over R, a ring with identity. A square matrix (aij) is said to be upper triangular if aij = 0 for i...

I have a set C: {0,1,3) and set D: {2,8} I have the product of sets CxD and DxC So for example CxD: {(0,2) , (0,8),} {(1,2), (1,8),} {(3,2),...

What I am really looking for here is an explanation as to why this process is actually able to prove that a statement is true for all values of n. Try to make your example non-mathematical and explain...