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Discrete Math

03/02/23

Use the element method to prove that a set is empty, prove or disprove that a set is a subset of another set, or prove that two sets are equal.

Let sets A, B, and C be defined as follows: A = {x ∈ Z : x = 63r + 2 for some integer r} B = {x ∈ Z : x = 7r + 2 for some integer r} C = {x ∈ Z : x = 9r + 2 for some integer r} . Prove or disprove... more

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Discrete Math

03/02/23

Compute unions, intersections, complements, and Cartesian products of sets.

Let S be the set of letters in your first name (or nickname), and let T be the set of letters in the word “discrete.” Write S and T in set-roster notation. Then compute S ∩ T.

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Discrete Math

02/27/23

Given a sequence defined recursively and its closed form, use strong mathematical induction to prove that the definitions are equivalent.

Suppose that a0, a1, a2, . . . is a sequence defined as follows:a0 = 2, a1 = 1, an = an−1 + 12an−2 for every integer n ≥ 2.Prove that an = (−3)n + 4n for every integer n ≥ 0.\p(0): (-3)^0+4^0=... more

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Discrete Math

02/24/23

Given a description in words, prove a statement using strong mathematical induction.

Suppose bottled water is sold only in sets of 3 bottles and sets of20 bottles. Let P(n) be the statement “n bottles of water can be sold.” Provethat P(n) is true for every integer n ≥ 38.

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Discrete Math

02/21/23

Prove Cassini’s identity?by induction

Prove Cassini’s identity: fn1 · fn+1 − (fn)2 = (−1)n for any n ≥ 2, there fn is the n-th Fibonacci number.

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Discrete Math

02/21/23

Help proving this by induction?

Consider a sport in which teams can score two types of goals, worth either 3 points or 7 points. For example, Team Miners might (theoretically speaking) score 32 points by accumulating, in... more

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Discrete Math

02/21/23

How do you prove this by induction?

Prove Bernoulli’s inequality by induction: For an arbitrary x ∈ R, such that x ≥ 1, prove by induction on n that (1 +x)n ≥ 1+nx for any positive integer n.

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Discrete Math

02/21/23

How do you prove this by induction?

Prove the following claim holds ∀n ∈ Z≥0 by induction on

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Discrete Math Math

02/20/23

What are permutations in Cryptography and how do you compute the product of multiple ones?

When there is a grouping of numbers how do you find the integer number that is equal to the product of two permutations? How do you solve and set it up?

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Discrete Math

02/17/23

Use the formula for the sum of the first n integers and/or the formula for the sum of a geometric sequence to evaluate summations and write them in a closed form.

Use the formula for the sum of the first n integers and the formulafor the sum of a geometric sequence to evaluate(7^2 − 5) + (7^3 − 10) + (7^4 − 15) + · · · + (7^2023 − 10110).Do not compute... more

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Discrete Math

02/17/23

Given a description in words, prove a statement using strong mathematical induction.

At a meeting of an organization, people want to split into smallgroups for an activity, with 3 or 4 people in each group. Let P(n) be thestatement “It is possible to arrange n people into groups,... more

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Discrete Math

02/16/23

Count number of binary strings that satisfy some conditions?

Let b be binary string of length r < n, b doesnt contain any adjacent 0s or 1s. Count number of binary string of length n that if we repeatedly apply these operations 1) 11 =1, 2) 00=0. b doesnt... more

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Discrete Math

02/16/23

Prove by induction that every integer n, n >=0, can be represented by 5a + 7b for a,b in Z

I'm having trouble approaching this by induction.I prove the base case in that if n = 0, 5a + 7b = 5(0) + 7(0) = 0I assume that 5a + 7b = n is true, then I try to show that it holds true for n+1.... more

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Discrete Math

02/09/23

Show that 0.0223 repeating is a rational number. Let x = 0.0223

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Discrete Math

02/09/23

Negate: If 15 | x, then 3 | x and 5 | x.

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Discrete Math Logic

02/04/23

Construct a field with 5 elements. Draw the tables of addition and multiplication.

Construct a field with 5 elements. Draw the tables of addition and multiplication.Hint 1. Let the elements of such a field be {0, 1, a, b, c}.Hint 2. use the cancellation rules, you may use the... more

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Discrete Math

01/05/23

Elimination Dice Roll Game

What are the odds and or probability of winning this game? How it works: Roll two 6 sided dice for 11 rounds. You are eliminated if you roll over the highest number for the round. Round one # is... more

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Discrete Math Math Calculus Chemistry

11/27/22

need help with math

I've been stuck on these problems for a while.Use the given transformation to evaluate the integral. ∫∫R 8xy dA, where R is the region in the first quadrant bounded by the lines y = 1x/3 and y = 2x... more

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Discrete Math Math

11/27/22

how many 4- digit can be formed?

Using the digits 1, 2, 3 and 5, how many 4-digit numbers can be formed if :the first digit must be 1 and repetition of the digits is allowed?the first digit must be 1 and repetition of the digits... more

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Discrete Math Math Physics Physics

11/25/22

please help with physics problem

A 530 lines/mm diffraction grating is illuminated by light of wavelength 540 nm. How many bright fringes are seen on a 3.5- m -wide screen located 2.2 m behind the grating?Please help

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Discrete Math Math Calculus Physics

11/22/22

help needed with math problem

Find the absolute maximum and minimum values of f on the set D. f(x, y) = 2x3 + y4 + 2 D = (x, y) | x2 + y2 ≤ 1 I'm stuck on this problem. The answers are the absolute max value is 4 and the... more

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Discrete Math

11/17/22

Proof with sigma notaion

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Discrete Math

11/17/22

True or false with Big O Notation,

1. True or false: a. 14n + 12n^2 + 4 ∊ O(n^2 ) b. n^n ∊ O(2^n ) c. n log₂ n ∊ O(n log₅ n) d. n log^2 n ∊ O(n log n) e. 9n / (3 log n) ∊ O(n)Note: log^k n = (log n)^K

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Discrete Math Math

11/04/22

Explain how to take the logical negation of the precise definition of continuity.

Explain what this statement means in plain English. I am really struggling with understanding this topic

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Discrete Math Logic

11/02/22

If 𝑎 and 𝑏 are integers for which 𝑎|𝑏 and 𝑏|𝑎, then 𝑎=±𝑏.

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Use the element method to prove that a set is empty, prove or disprove that a set is a subset of another set, or prove that two sets are equal.

Compute unions, intersections, complements, and Cartesian products of sets.

Given a sequence defined recursively and its closed form, use strong mathematical induction to prove that the definitions are equivalent.

Given a description in words, prove a statement using strong mathematical induction.

Prove Cassini’s identity?by induction

Help proving this by induction?

How do you prove this by induction?

How do you prove this by induction?

What are permutations in Cryptography and how do you compute the product of multiple ones?

Use the formula for the sum of the first n integers and/or the formula for the sum of a geometric sequence to evaluate summations and write them in a closed form.

Given a description in words, prove a statement using strong mathematical induction.

Count number of binary strings that satisfy some conditions?

Prove by induction that every integer n, n >=0, can be represented by 5a + 7b for a,b in Z

Show that 0.0223 repeating is a rational number. Let x = 0.0223

Negate: If 15 | x, then 3 | x and 5 | x.

Construct a field with 5 elements. Draw the tables of addition and multiplication.

Elimination Dice Roll Game

need help with math

how many 4- digit can be formed?

please help with physics problem

help needed with math problem

Proof with sigma notaion

True or false with Big O Notation,

Explain how to take the logical negation of the precise definition of continuity.

If 𝑎 and 𝑏 are integers for which 𝑎|𝑏 and 𝑏|𝑎, then 𝑎=±𝑏.

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