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Is the following sentence a logical proposition? Justify your answer. If it is a proposition, determine its truth value.Consider the conditional statement "Every week having seven days is necessary... more

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Discrete Math Discrete Mathematics

08/29/20

Proof of the question

Assume that x ∈ Q and y ∈ R∖Q. For each of the following, either prove the statement is true, or provide a counterexample to prove the statement is false.(a) ∀x, y, x + y is rational.(b) ∀x, y, x... more

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Discrete Math Discrete Mathematics

08/29/20

Proof of the question

Prove that { 6x | x ∈ Z}={ 2x | x ∈ Z } ∩ { 3x | x ∈ Z }.Hint: Try proving set containment in both direction (⊆ and ⊇).

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Discrete Math

08/21/20

Which of the following sets are equal? (Select all that apply.) [selections on description below]

A = {3, 4, 5}B = {x R| 2 ≤ x < 6}C = {x R| 2 < x < 6}D = {x Z| 2 < x < 6}E = {x Z+| 2 < x < 6}

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Discrete Math

08/21/20

Let S = {0, 1}. List all the strings of length 4 over S that contain three or more 1's. (Enter your answer in set-roster notation.)

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Discrete Math

08/04/20

Where 𝜑(𝑛) is Euler’s Totient Function, find

a. 𝜑(77) b. 𝜑(751)

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Discrete Math

08/04/20

Prove the following:

𝐸𝑣𝑒𝑟𝑦 𝑝𝑒𝑟𝑓𝑒𝑐𝑡 𝑠𝑞𝑢𝑎𝑟𝑒 𝑖𝑠 𝑒𝑖𝑡ℎ𝑒𝑟 𝑎 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑒 𝑜𝑓 4 𝑜𝑟 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑜𝑟𝑚 4𝑛 + 1 𝑓𝑜𝑟 𝑠𝑜𝑚𝑒 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑛. (try proof by cases, since an integer is either even or odd, do one proof where 𝑛 is even, then do another... more

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Discrete Math

08/04/20

Solve for x, verify by division.

a. 3 𝑥 ≡ 1 (𝑚𝑜𝑑 11) 𝑏. 162𝑥 ≡ 1 (𝑚𝑜𝑑 5)

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Discrete Math

08/04/20

Show the following number 𝑁 is either possibly prime or definitely composite using the two parts of the Fermat Primality test.

𝑁 = 19

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Discrete Math

08/04/20

Find the multiplicative inverse of 𝑎 𝑚𝑜𝑑 𝑛 (𝑎 −1 )

13(𝑚𝑜𝑑 31)

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Discrete Math

08/04/20

Do the following congruence equations have solutions? If so how many? Do not solve the equations.

a. 4𝑥 ≡ 7(𝑚𝑜𝑑 16)b. 5𝑥 ≡ 12(𝑚𝑜𝑑 32)

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Discrete Math

08/04/20

Use the EEA to find integers 𝑥 and 𝑦 such that :

84𝑥 + 33𝑦 = gcd(84,33)

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Discrete Math

08/04/20

Which of the following numbers are prime? Show why.

a. 1731 b. 21977

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Discrete Math

08/04/20

Use the EEA to find integers 𝑥 and 𝑦 such that:

300𝑥 + 222𝑦 = gcd(300,222)

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Discrete Math

07/29/20

Discrete Math TY!

Q1:A>C, B>D ⊢ (A∧B)>(C∧D)Q2:AvB, A>C, B>D ⊢ CvD

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Discrete Math

07/28/20

Find gcd (1258, 451). Use the Euclidean algorithm.

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Discrete Math

07/28/20

Prove the following: 𝐹𝑜𝑟 𝑛 ∈ ℤ, 𝑝𝑟𝑜𝑣𝑒 𝑡ℎ𝑎𝑡 𝑖𝑓 𝑛 𝑖𝑠 𝑒𝑣𝑒𝑛,𝑡ℎ𝑒𝑛 𝑛 3 + 2𝑛 𝑖𝑠 𝑑𝑖𝑣𝑖𝑠𝑖𝑏𝑙𝑒 𝑏𝑦 4.

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Discrete Math

07/28/20

Two integers a and b are said to be relatively prime (or coprime) if the gcd is equal to what number?

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Discrete Math

07/28/20

Give a brief statement(definition) of the Fundamental Theorem of Arithmetic. Represent the number 1092 by the theorem.

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Discrete Math

07/28/20

Find lcm (45, 567) Use the Euclidean algorithm.

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Discrete Math

07/28/20

Find gcd( 1180, 482). Use the Euclidean algorithm.

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Discrete Mathematics Questions

Discrete Mathematics Questions

Discrete Mathematics Questions

Discrete Mathematics Questions

Is the following sentence a logical proposition?

Proof of the question

Proof of the question

Which of the following sets are equal? (Select all that apply.) [selections on description below]

Let S = {0, 1}. List all the strings of length 4 over S that contain three or more 1's. (Enter your answer in set-roster notation.)

Where 𝜑(𝑛) is Euler’s Totient Function, find

Prove the following:

Solve for x, verify by division.

Show the following number 𝑁 is either possibly prime or definitely composite using the two parts of the Fermat Primality test.

Find the multiplicative inverse of 𝑎 𝑚𝑜𝑑 𝑛 (𝑎 −1 )

Do the following congruence equations have solutions? If so how many? Do not solve the equations.

Use the EEA to find integers 𝑥 and 𝑦 such that :

Which of the following numbers are prime? Show why.

Use the EEA to find integers 𝑥 and 𝑦 such that:

Discrete Math TY!

Find gcd (1258, 451). Use the Euclidean algorithm.

Prove the following: 𝐹𝑜𝑟 𝑛 ∈ ℤ, 𝑝𝑟𝑜𝑣𝑒 𝑡ℎ𝑎𝑡 𝑖𝑓 𝑛 𝑖𝑠 𝑒𝑣𝑒𝑛,𝑡ℎ𝑒𝑛 𝑛 3 + 2𝑛 𝑖𝑠 𝑑𝑖𝑣𝑖𝑠𝑖𝑏𝑙𝑒 𝑏𝑦 4.

Two integers a and b are said to be relatively prime (or coprime) if the gcd is equal to what number?

Give a brief statement(definition) of the Fundamental Theorem of Arithmetic. Represent the number 1092 by the theorem.

Find lcm (45, 567) Use the Euclidean algorithm.

Find gcd( 1180, 482). Use the Euclidean algorithm.

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