Ask Question, Ask an Expert

+1-415-315-9853

info@mywordsolution.com

Ask Math Expert


Home >> Math

problem 1: Let A be a nonempty set. Define the relation R on the nonempty subsets of A by (X; Y) ε R if and only if X ∩ Y ≠ Φ. Determine whether R is (i) reflexive, (ii) symmetric, (iii) antisymmetric, (iv) transitive.

problem 2: Let n = (abc)7. Show that n ≡ a + b + c (mod 6).

problem 3: Use congruences to prove that 4|32n   1 for all integers n ≥ 0.

problem 4: Let a0, a1, ..... be the sequence recursively defined by a0 = 1, and an = 3 + an-1for n ≥ 1.

a) Compute a1, a2, a3 and a4.
b) Guess a formula for an, n ≥ 0.
c) Use induction to prove that your formula is correct.

problem 5: Define a sequence bn by b0 = 5, b1 = 9, and bn = bn-1 + bn-2 for n ≥ 2.

Use strong induction to prove that bn < 5 . 2n for all n ≥ 1.

problem 6: Find the number of six-digit positive integers that can be formed using the digits 1, 2, 3, 4, and 5 (each of which may be repeated) if the number must begin with two even digits or with two odd digits.

problem 7: In a collection of 30 di§erent birds, 15 eat worms, 18 eat fruit, and 12 eat seeds. Exactly 8 eat worms and seeds, 8 eat worms and fruit, 7 eat fruit and seeds, and 4 eat all three types. Two birds are selected at random. What is the probability that:

a) both birds eat at least one of these food groups?
b) both eat at least one common food group?
c) both eat all three food types?

problem 8: How many ways can six men and three women form a line if no two women may stand behind each other?

Math, Academics

  • Category:- Math
  • Reference No.:- M91150

Have any Question? 


Related Questions in Math

A hospitals revenue in millions of dollars is projected to

A hospital's revenue (in millions of dollars) is projected to be R(x) = 9x2 + 7x + 81 and its costs (in millions of dollars) are projected to be C(x) = -2x2 - 10x - 14 where x represents the number of years into the futu ...

What are the criteria of a nursing theoryhow has the role

What are the criteria of a nursing theory? How has the role of Nurse Practitioner changed over time?

Find the values of the indicated functions given cot theta

Find the values of the indicated functions. Given cot θ =0.7350, find csc θ and sec θ. (Do not round until the final answer. Then round to three decimal places as needed.)

Coin 1 has pheads 06 and coin 2 has pheads 05 coin 1 is

Coin 1 has P(Heads) = 0.6, and Coin 2 has P(Heads) = 0.5. Coin 1 is flipped until the first time Tailsappears. Then Coin 2 is flipped until the first time Tails appears. This process is continued, flipping andswitching e ...

1 why is it necessary to account for the order of a matrix

1. Why is it necessary to account for the order of a matrix when adding or subtracting matrices? 2. Explain the conditions necessary to multiply two matrices, each of a different order. What does the scalar multiplicatio ...

For this discussion board you will each take the role of

For this discussion board, you will each take the role of teacher. You will each choose ONE of the following rules or properties of exponents and teach it to the class (i.e., explain it in your own words and give an exam ...

As jobs dry up because of the spread of artificial

As jobs dry up because of the spread of artificial intelligence, some have suggested giving everyone a paycheck which is enough to cover housing, food, health care and other basic needs. This is known as universal basic ...

Sasha and tim are playing a dice game that involves rolling

Sasha and Tim are playing a dice game that involves rolling two 6-sided dice. According to the rules, if a player rolls a sum that is greater than 8 or a multiple of 5, the player gets a bonus of 100 points. The probabil ...

You are tasked with choosing a corporation and discussing

You are tasked with choosing a corporation and discussing the importance of ethics and social responsibility in relation to that particular corporation. Think about the stakeholders associated with the corporation and ho ...

1 find an equation of the parabola that has a focus at

1. Find an equation of the parabola that has a focus at (3,11)and a vertex at (3,9): y= Find an equation of its directrix: y= 2. Find the equation for the parabola that has its focus at the (-41/4,-6)and has directrix at ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

Section onea in an atwood machine suppose two objects of

SECTION ONE (a) In an Atwood Machine, suppose two objects of unequal mass are hung vertically over a frictionless

Part 1you work in hr for a company that operates a factory

Part 1: You work in HR for a company that operates a factory manufacturing fiberglass. There are several hundred empl

Details on advanced accounting paperthis paper is intended

DETAILS ON ADVANCED ACCOUNTING PAPER This paper is intended for students to apply the theoretical knowledge around ac

Create a provider database and related reports and queries

Create a provider database and related reports and queries to capture contact information for potential PC component pro

Describe what you learned about the impact of economic

Describe what you learned about the impact of economic, social, and demographic trends affecting the US labor environmen