Prove that an integer n>1 is a prime if and only if all of the binomial coefficients C(n,k) (1<k<n) are divisible by n
Prove that an integer n>1 is a prime if and only if all of the binomial coefficients C(n,k) (1<k<n) are divisible by n
Suppose that R and S are equivalence relations on a set A. Prove that the relation R ∩ S is also an equivalence relation on A.E
Proof by mathematical induction that for every integer h ≥ 0 there exists binary tree of height h with 2h leaves.
Proof by mathematical induction that for every integer h ≥ 0 there exists binary tree of height h with 2h leaves.
suppose there are 12 seniors and 10 juniors in a schools honor society. ten honor students must be chosen to attend a conference. the conference organizers require that a school send more seniros...
Assume you have a predicate P(n). You know that P(8) is true and that P(k) → P(k + 5). For what values of n do you know that P(n) is true? Write your answer using mod arithmetic
Proof by induction that maximum number of leaves in m-subtree of height h is at least mh
Suppose a machine on average takes 108 seconds to execute a single algorithm step. What is the largest input size for which the machine will execute the algorithm in 2 seconds assuming the number...
What is the minimum height of a full binary tree T which has nodes n(T) = 2k-1 for k= 1, 2, ... ?
Prove the following proposition using resolution. [(p → q) ∧ (q → r) Λ p] → r Show first the conjunctive normal form of the negation of the proposition...
Let the sets be the following. A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} B = {a, b, c, Ø, {1}, {2}} C = {a, b, {c}} Show a number or a simple expression that defines a number...
I really need help on these types of questions. I just don't understand how to do them. I don't even understand what math this is lol (algebra 1,2 or geometry). Please help and please tell...
how many odd three digit numbers can be made using the digits 1,2,3,4,5,7?
We have to recurrence relation an = 2an-1 - an-2. Find a2 and a3 if: a) a0 = 1 and a1= 1? b) a0 = 0 and a1 = 0?
Find a closed form for these summations? n=100 a) ∑ 1/2 i=1 n=5 b) ∑ 1/3 &n...
Please Show the solution the premise and the laws that you used i can't get it thanks number two is the most i need to have an answer . 1.) 1. (M v N) → O ...
(a) Please count how many functions f : D → {0, 1} can be defined if the domain D is a finite set with the cardinality |D| = n. (b) Can you find a bijection between the set of all such...
let T = {(x,y) ∈ R x R(real numbers) | y = √x / (√(x-3)) Let D = {y ∈ R, | (x,y) ∈ T for x ∈ R}. for each one, decide if true or false a) 1/4 ∈ D b) 4 ∈ D why...
Using mathematical induction, prove that for any integer n, with n≥1, n(n2-1)(n+2) is divisible by 4.
A company conducts a survey every spring to measure the morale of its employees. A group to be surveyed is randomly selected from all employees who have been with the company for exactly 5 years....