Number Sets

Number sets can be described as collections of mathematical entities that share specific characteristics. Prominent sets encompass Natural Numbers (numbers used for counting), Whole Numbers (which include the number zero), Integers (comprising of both positive and negative numbers as well as zero), Rational Numbers (expressed as fractions), Irrational Numbers (decimals that do not repeat) and Real Numbers (an amalgamation of both rational and irrational numbers).

Finding the Intersection of Sets

Find the intersection of the solution sets of the following linear equations:

2 x - 3 y = 6

and

5 x + 4 y = 20

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Finding the Union of Number Sets

Let

S = {1, 2, 3}

and

T = {3, 4, 5}

be two sets of numbers. What is the union of these two sets?

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Determining if a Set is a Subset of Another Set

Let

A = {1, 2, 3}

and

B = {1, 2, 3, 4, 5}

be two sets of numbers. Is set

A

a subset of set

B

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Finding the Set Complement of Two Sets

Let

A = {1, 2, 3, 4, 5}

and

B = {3, 4, 5, 6, 7}

be two sets in the universal set

U = {1, 2, 3, 4, 5, 6, 7}

. Find the complement of the set

A ⋃ B

U

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Finding the Power Set

Let's consider the set

S = {1, 2}

. What is the power set of

S

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Finding the Cardinality

Let's say we have a set of linear vectors

V

in a 3-dimensional space, where

V = {v_{1}, v_{2}, v_{3}, v_{4}}

. The vectors are defined as follows:

v_{1} = (1, 0, 0)

v_{2} = (0, 1, 0)

v_{3} = (0, 0, 1)

and

v_{4} = (1, 1, 1)

. What is the cardinality of the base of vector space that these vectors span?

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Finding the Cartesian Product of Two Sets

Let

A = {1, 2}

and

B = {3, 4}

. Find the Cartesian product of these two sets (

A \times B

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Determining if a Set is a Proper Subset of Another Set

Let's consider two sets in the linear algebra context. Set A contains the vectors [1, 2], [3, 4] and set B contains the vectors [1, 2], [3, 4], [5, 6]. Is set A a proper subset of set B?

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Number Sets

Finding the Intersection of Sets

Finding the Union of Number Sets

Determining if a Set is a Subset of Another Set

Finding the Set Complement of Two Sets

Finding the Power Set

Finding the Cardinality

Finding the Cartesian Product of Two Sets

Determining if a Set is a Proper Subset of Another Set

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