149 Answered Questions for the topic discrete mathematics

An urn contains eight red balls, eight white balls, and eight blue balls, and sample of four balls is drawn at random without replacement.

Compute the probability that all of the balls in the sample are the same color. (Round your answer to four decimal places.)

Hard problem, discrete math.

If x+y+z=3 , x2+y2+z2=4, and x3+y3+z3=5 what is x, y, and z? I found that none of them can be equal or greater than 2.

Prove by Induction question, 2+6+18+...+ 2.3^n-1 = (3^n)-1

Can anyone help me solving this problem, Im really really lost. Thank you

Direct proof question, "The product of an even integer and an odd integer is even".

I didnt understand  Let say X = 2a +1 while y = 2b+1   Why you need to multiply xy rather x+y, as you can see below: XY = (2a+1)(2y+1) <- correct X+Y = 2a+1+2y+1 <- Incorrect   Can you... more

Counting / Permutation & Combination

Given two positive integers n and k with the same parity, count the number of sets S = { 0< s1 < s2 < ... < sk = n }, such that s1, s3, ... are odd numbers and s2, s4, ... are even numbers more

Homework help for discrete

Suppose f: integer(z) to integer(z) is a function with the property that f(a+b) = f(a) + f(b) for every two integers a and b. Prove that if f(c) is even for some odd integer c then f(x) is even for... more

Discrete math Problem!

Suppose f: integer(z) to integer(z) is a function with the property that f(a+b) = f(a) + f(b) for every two integers a and b. Prove that if f(c) is even for some odd integer c then f(x) is even for... more

True or False: If false, give a counter example if true write a proof. Discrete Math

For all positive integers m and n, with m<n if m divides (35n) then either m divides 35 or m divides n

Find a polynomial function f(n) such that f(1), f(2), ... , f(8) is the following sequence.

4, 12, 20, 28, 36, 44, 52, 60 f(n) =___ans________

Given the following definition, compute Q(5).

   Q(n) = {0                                             if n = 0                  1                                             if n=1                ... more

Every year, Alice gets a raise of $3,000 plus 6% of her previous year's salary.

Every year, Alice gets a raise of $3,000 plus 6% of her previous year's salary. Her starting salary is $20,000. Give a recurrence relation for S(n), Alice's salary after n years, for n ≥ 0. S(n) =... more

A={1+1(-n)2/n E n} Determine all elements

Determine all elements A={1+1(-n)2/ n E n}

a={xEz+//x+2<5-} determine all elements

prime numbers a={xEz+//x+2<5-} determine all elements

Prove the statement is true using mathematical induction: 2n-1 ≤ n!

Prove the statement is true using mathematical induction: 2n-1 ≤ n!

Create a logic circuit for the logical proposition.

Create a logic circuit for the logical proposition P∨Q∧¬P

Home Work Assignmet

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 + 1 ?   3. Let r =... more

How does P(X<= a) + P(X > a) = 1 becomes [P(X <= a) >= 1?

I would have to include pictures for it.

let d=(a,b) then a|bc if and only if a/d is a divisor of c

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

Composition of relations on the real numbers.

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 each relation below. (Hint:... more

Relations and Functions (Home Work)

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 = [1  1               1  0]... more

Define functions f, g, h, all of which map from R -> R. (Discrete Mathematics, Functions)

f(x) = -(x - 1)g(x) = 2x2h(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)?

n is a sum of two squares if n = a2 + b2 for integers a&b. If x&y are both sums of 2 squares, prove that xy is a sum of 2 squares.

Layout of the step by step procedure of solving the problem is needed  please.

Consider the surjective function cos: R ? [-1, 1] and let ~ be the associated equivalence relation x ~ y ?? cos x = cos y. Find the Equivalence Class

Consider the surjective function cos: R → [−1, 1] and let ∼ be the associated equivalence relationx ∼ y ⇐⇒ cos x = cos y.   Describe the equivalence classes of ∼. (b) Do the analogous exercise... more

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