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. 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 +...

I would have to include pictures for it.

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

The diagram below shows a directed graph: http://imgur.com/a/fxqVD (a) Is <d, b, c, g, c, f, e, c, d> a circuit in the graph? Is it a cycle? (b) What is the longest cycle in...

The diagram below shows a directed graph: http://imgur.com/a/fxqVD (a) Is <d, b, c, g, c, f, e, c, d> a circuit in the graph? Is it a cycle? (b) What is the longest cycle in the...

Here are two relations defined on the set {a, b, c, d}: S = { (a, b), (a, c), (c, d), (c, a) } R = { (b, c), (c, b), (a, d), (d, b) } Write each relation as a set of ordered pairs. (a)...

In a small town a bank (b), school (s), town hall (t), and shopping mall (m) are connected by a series of narrow one-way streets; a street from the town hall to the bank, one from the bank to the...

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 ...

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...

1. Use truth tables to prove that (p ∧ ¬q) ∨ ¬(q ∧ r) ∨ (r ∧ p) ⇔ p ∨ ¬q ∨ ¬r (1) 2. Write the...

Any single project must have at least 3 team members but no more than 4. There are currently 37 available team members in the company, all of whom are cross-trained to serve any role on any given...

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)...

Discrete metric spaces. Suppose that d is the discrete metric on E. Show that (x n ) is convergent if and only if it is ultimately stationary, that is, if and only if it has the form (x 1 , x2 ,...

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. Describe the equivalence classes of ∼...

We are told to find injection between the set D and the set of natural numbers N but I'm not really sure how to do that in this case

Show that the set of all integers divisible by 8 is countable.

Type | Probability 1 ton | 0.25 2 tons | 0.06 5 tons | 0.01 10 tons | 0.11 20 tons | 0.57 An appliance dealer sells 5 types of air conditioners. The above...

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...

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