set notation

States that begin with the letter C Our set has 3 elements: {California, Colorado, Connecticut}

set of all continents Our set of 7 elements is below: {Africa, Antarctica, Asia, Australia/Oceania, Europe, North America, and South America.}

x is a woman who served as US president before 2000 No woman US presidents before 2000, so we have the empty set. x = {}

n is a factor of 16 List out factor of 16: 1 * 16 2 * 8 4 * 4 From the list above, we take the 5 unique factors and build a set for n: n = {1, 2, 4, 8, 16}

A belongs to Both X and Y What this means is Element A belongs to Set X and Set Y. We write this as follows A is an element of X is written as A ∈ X A is an element of Y is written as A ∈ Y A ∈ X & A ∈ Y

(A^C)^C we read this as The complement of the Complement of Set A The complement of set A is anything NOT in A. But the complement of the complement is anything NOT NOT IN A. Which is just A

B is the set of vowels in the English alphabet B = {a, e, i, o, u}

A={2,3} B={4,5} find a union b A union B is everything in A and B A U B = {2, 3, 4, 5}

Set B is the set of distinct letters in the word GIFT Set B has 4 elements below: B = {G, I, F, T}

{x | x is an even integer between -3 and 5} We list even integers out in this range: {-2, 0, 2, 4}

A U ∅ = A Let x ∈ S, where S is the universal set. First we show that if A ∪ Ø ⊂ A. Let x ∈ A ∪ Ø. Then x ∈ A or x ∈ Ø. by definition of the empty set, x cannot be an element in Ø. So by assumption, x ∈ A ∪ Ø, x must be in A. So A ∪ Ø ⊂ A. Next, we show that A ⊂ A ∪ Ø. This is true...

Set D is the set of two-digit even numbers less than 67 that are divisible by 5 two-digit numbers start at 10. Divisible by 5 means the last digit is either 0 or 5. But even numbers don't end in 5, so we take the two-digit numbers ending in 0: D = {10, 20, 30, 40, 50, 60}

The planets in the solar system as set G. Since Pluto was removed as a planet, we have the following set G with 8 elements: G = {Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune}

All the colors of the rainbow You can find this with the acronym: ROYGBIV Red Orange Yellow Green Blue Indigo Violet Written as a set, we have 7 elements: {Red, Orange, Yellow, Green, Blue, Indigo, Violet}

L is the set of letters in the word Mississippi We want only unique letters, so we have: L = {I, M, P, S}

Months with 31 days as set M Our cardinality of this set is 7, as show below: {January, March, May, July, August, October, December}

set of vowels in the word ALGEBRA Vowels are A, E, I, O, U. For ALGEBRA, we have A, E, A We group the 2 A's together, so our answer is: {A, E}

Set of 2 digit even numbers less than 40 Knowns and givens: 2 digit numbers start at 10 Less than 40 means we do not include 40 Even numbers are divisible by 2 {10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38}

D is the set of days in the week. D = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}

The set of all letters in the word p lus is The cardinality of this set is 4 with the elements below: {p, l, u, s}