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
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}
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}