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 ∼...

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...

http://imgur.com/a/gG7dj I am stuck on the very bottom problem. I have defined k1-9 and r1-9. If there is a better way way to upload a picture then please tell me ...

Let A, B and C be different sets containing letters of the alphabet. Explain why there must exist some letter that is either contained in exactly one of the sets or contained in exactly two...

Letfbe a homomorphism from the commutative ring R onto the ring R'. If I and J are ideals of R, verify each of the following: a) f(I intersect J) subset f(I) intersect f(J), with equality...

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)...

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),...

A⊆B ----------------- |(P(A))| ≤ |(P(B))| Not sure if the bottom symbols are right but its the cardinality of power set A and the cardinality of power set B The sets are...

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...

Suppose we are given the following program segment: F(x) = 0 Input n For x = 1 to x = n y = x*(x+3)+2 Print y Next x 1. Determine the number of steps...

How would you explain to this person why it is that induction actually does work. In my follow up responses to you, I may ask you questions that your friend might as in response to your explanation...

F(x) = 0 Input n For x = 1 to x = n y = x*(x+3)+2 Print y Next x 1. Determine the number of steps the program will execute before entering the loop. 2. Determine...

let 〈xn〉n=1...∞ be a sequence satisfying xn+1=xn-xn-1 for each n. Prove that xn+6=xn for all n belonging to N using the below formula xn=p((1+i(sqrt3))/2)n+q((1-i(sqrt3))/2)n p...

Given the information x1=1 and x2=2, and ∀ n≥2, xn+1=4xn-5xn-1, find explicitly the values of p,q which make xn=p(2+i)n+q(2+i)n for every n. I am really having...

Pigeon hole principle

use the well-ordering principle. Please help with this question, it's a practice problem, I just can't figure out. Thank you!

let m,n belong to N, and m,n>1, prove that mn< (m+n)choose 2 Please help. Thank you!

For a 2 coin toss experiment, what are the set of events that are statistically independent when you assume: a) equally likely outcomes b) not equally likely outcomes

let n∈N. if a,b,c,d ∈ N and a≡b (mod n) and c≡d (mod n) prove that ac≡bd (mod n). Please, any help would be greatly appreciated. This is a study question on my study guide and I'm having...

security codes are made of 3 letters followed by four single digit numbers. How many different 7 character security codes can be made if none of the letters can repeat and the first digit must be...