 Discrete Mathematics at Columbia College (SC) | Flashcards & Summaries

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What are curly braces used for?

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When you want to write the elements of your set directly

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What is Set Builder notation useful for?

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It is useful when it is easier to describe "verbally" the contents of a set.

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What is an example of a "universal set"?

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A set "U" of which all other sets being discussed are subsets is referred to as a universal set.

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Divisibility tip for the number 9

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A number n is divisible by 9 if the sum of the digits of n is divisible by 9

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Claim 3|12

Claim 5|125

Claim 7|23

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3 * c = 12      c = 4

5 * c = 125    c = 25

7 * x = 23      c = x

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Divisibility tips for 2

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2: 1's digit is divisible by 2

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Divisibility tips for 3

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The sum of the digits must be divisible by 3

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Divisibility tip for the number 6

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Rule for #2 and #3 must apply

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For the modulo operator, if n < 0, what is a trick you can do to quickly get your answer?

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Repeatedly add m to itself until you get a positive #.

Ex: - 20 mod 3

- 20 = 3 = -17

-17 + 3 = -14

- 14 + 3 = - 11

- 11 + 3 = - 8

- 8 + 3 = - 5

- 5 + 3 = - 2

- 2 + 3 = 1

- 20 mod 3 = 1

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Solve 12 - 18 mod 5

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((12 mod 5) - (18 mod 5)) mod 5

= (2 - 3) mod 5

= - 1 mod 5 (add 5 to 1)

= 4

12 - 18 mod 5 = 4

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Define the rule for multiplication in modular arithmetic

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(n * m) mod k = ((n mod k) * (m mod k)) mod k

Ex:

12 * 18 mod 5

= ((12 mod 5) * (18 mod 5)) mod 5

= (2 * 3) mod 5

= 6 mod 5

= 1

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Define a prime number.

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A natural number n is prime if the only natural numbers that divide n are 1 and n.

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• 161 Studierende
• 9 Lernmaterialien

## Beispielhafte Karteikarten für deinen Discrete Mathematics Kurs an der Columbia College (SC) - von Kommilitonen auf StudySmarter erstellt!

Q:

What are curly braces used for?

A:

When you want to write the elements of your set directly

Q:

What is Set Builder notation useful for?

A:

It is useful when it is easier to describe "verbally" the contents of a set.

Q:

What is an example of a "universal set"?

A:

A set "U" of which all other sets being discussed are subsets is referred to as a universal set.

Q:

Divisibility tip for the number 9

A:

A number n is divisible by 9 if the sum of the digits of n is divisible by 9

Q:

Claim 3|12

Claim 5|125

Claim 7|23

A:

3 * c = 12      c = 4

5 * c = 125    c = 25

7 * x = 23      c = x

Q:

Divisibility tips for 2

A:

2: 1's digit is divisible by 2

Q:

Divisibility tips for 3

A:

The sum of the digits must be divisible by 3

Q:

Divisibility tip for the number 6

A:

Rule for #2 and #3 must apply

Q:

For the modulo operator, if n < 0, what is a trick you can do to quickly get your answer?

A:

Repeatedly add m to itself until you get a positive #.

Ex: - 20 mod 3

- 20 = 3 = -17

-17 + 3 = -14

- 14 + 3 = - 11

- 11 + 3 = - 8

- 8 + 3 = - 5

- 5 + 3 = - 2

- 2 + 3 = 1

- 20 mod 3 = 1

Q:

Solve 12 - 18 mod 5

A:

((12 mod 5) - (18 mod 5)) mod 5

= (2 - 3) mod 5

= - 1 mod 5 (add 5 to 1)

= 4

12 - 18 mod 5 = 4

Q:

Define the rule for multiplication in modular arithmetic

A:

(n * m) mod k = ((n mod k) * (m mod k)) mod k

Ex:

12 * 18 mod 5

= ((12 mod 5) * (18 mod 5)) mod 5

= (2 * 3) mod 5

= 6 mod 5

= 1

Q:

Define a prime number.

A:

A natural number n is prime if the only natural numbers that divide n are 1 and n. ### Erstelle und finde Lernmaterialien auf StudySmarter.

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