147 Answered Questions for the topic discrete mathematics

show that R x Zn has an identity element.

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) = (xy + ay + bx,... more

Ideal and subring

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 > j and strictly... more

Recursion and Recurrence Relations (Home Work)

1.  Let αk = 3k  + k - 2 for all k ≥ 0.a.  Write down the values of α1, α2 and α3.b.  Write down the values of A(1), A(2) and A(3) defined by the recurrence relation: A(0) = -1, A(k) = 3A(k-1) - 2k... more

discerete mathematics

h) Suppose Marck (M) and Erick (E) are playing a tennis tournament such that the first person to win two games in a row or who wins a total of three games wins the tournament. Find the number of... more

i ned solution of this please help

Show that p↔q≡(p→q)^(q→p)

please help me solve this

h) Suppose Marck (M) and Erick (E) are playing a tennis tournament such that the first person to win two games in a row or who wins a total of three games wins the tournament. Find the number of... more

please help me with the solution

b) Each student in liberal arts at some college has a mathematics requirement A and a science requirement B. a poll of 140 students shows that; 60 completed A, 45 completed B, 20 completed both A... more

Expected Value + Probability

Twenty distinct integers are arranged in a list in a random order, such that all 20! orderings are equally likely. Going down the list, one marks every number that is larger than all earlier... more

Seating arrangements of 7 boys and 5 girls in a row.

In how many ways can these boys and girls be arranged in a row if between two particular boys A and B there are no boys but exactly 3 girls?

Let p be a odd prime, If ord p (a) = h and h is even, then a^(h/2)= -1 mod p

Determine is, in general, true or false. Recall that auniversal statement is true if it is true for all possible cases while it is false if there is even onecounterexample. Be prepared to prove... more

10 Very challenging proof: Prove that for every natural number n, cos(nx) can be expressed as a polynomial in cos(x) of degree n

Pleas helm me with this. Its a practice problem, and I do not know how to do it. Thanks!

please help wit the problem below

prove that for every n∈N, ∑k2=(n(n+1)(2n+1))/6. Prove using mathematical induction

prove that there does not exist n belongs to N such that n congruent 2 (mod 4) and n congruent 4 (mod 8)

prove that there does not exist n∈N such that n≡2 (mod 4) and n≡4 (mod 8). Please help this was on my last exam but I was very lost and my professor did not have enough time to go over it in class.

Let n belong N. Define r:N2n --> N2n by r(x)= x+1 if x is odd, r(x)= x-1 if x is even. Prove that r is a bijection.

"N2n→ N2n" Just for clarification. Please help me! I have an exam I need to study for and my professor said something like this might show up on it. Thank you!

convert(1001111101101)2 to base 16

convert(1001111101101)2 to base 16

convert (7A3E)16 to binary

could you help me how can I convert (7A3E)16 to binary

Discrete Mathematics

A={ -4 ,-3 ,-2 ,-1 ,0 ,1 ,2 ,3 ,4} R is defined on A as follows: For All (m,n) ∈A,m R n ⇔ 5 | (m^2- n^2 )

For all real equations, prove f is decreasing if -f is decreasing

I believe the problem was to write a proof that proved For all real equations, prove f is decreasing if -f is decreasing

Probability of winning a laptop?

There is going to be a raffle in the College of Engineering and Computer Science. They are going to give away one prize. It willbe either a coffee mug, and old mouse, or a brand new Alienware... more

Proof by induction.

Proof by mathematical induction that for every integer h ≥ 0 there exists binary tree of height h with 2h leaves.

Proof by mathematical induction.

Proof by mathematical induction that for every integer h ≥ 0 there exists binary tree of height h with 2h leaves.

What is the minimum height height of a full binary tree?

What is the minimum height of a full binary tree T which has nodes n(T) = 2k-1 for k= 1, 2, ... ?

How many full binary tree's T, exist with the height:

How many full binary tree's T, exist with the height: a) h(T) = 1 b) h(T) = 3   Can someone please explain this to me? 

Prove the following proposition using resolution.

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. Then show a sequence of numbered... more

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