Language of Sets

Question 1

x ∈ S
x ∉ S

Answer 1

X is an element of S
X is not an element of S

Question 2

Let A = {1,2,3}, B = {3,1,2} and C = {1,2,1,2,3,2,1}, what are the elements of A, B and C?

Answer 2

1,2,3, since these are the elements of similarity.

Question 3

Let Un = {n, -1}, find U0.

Answer 3

U0 = {0, -0} = {0, 0} = {0}

Question 4

|

Answer 4

Such that
{x ∈ S | P(x)}
There exists an object.
{ n | n > 0 } = {1, 2, 3,…}

Question 5

{x ∈ R | -2 < x < 5}

Answer 5

x exists as a real number such that x is in-between -2 and 5.

Question 6

Subsets / ⊆

Answer 6

A base relation between sets.
If A and B are sets, then A is called a subset of B.
Written as A⊆B (for all elements in x, if x ∈ A then x ∈ B)

Question 7

⊄

Answer 7

Not a subset of
There is at least one element in which x ∈ A but x ∉ B

Question 8

A = {1, 2, 3} and B = {1, 2, 3, 4, 10}

Answer 8

A is a subset of B, but B is not a subset of A

Question 9

Ordered Pair

Answer 9

Specification that elements are in specific places (for example, (A, B). If a != b, then the first element has to be a and the second being b because it is specifically ordered). This means that pairs like (1,2) and (2,1) are not the same since they are not ordered the correct way, but pairs like (3squared, 2) and (9, 2) are the same because they are ordered with the same answers when simplified.

Question 10

Cartesian Product of A and B

Answer 10

A x B = {(a, b) | a ∈ A and b ∈ B}
A x B is the set of all ordered pairs where a is in A and b is in B.

Question 11

Find A x B if A = {1,2,3} and B = {u,v}

Answer 11

A x B = {(1, u), (2, u), (3, u), (1, v),(2,v),(3,v)}

Question 12

Cartesian Plane

Answer 12

R x R
Ordered pairs (x, y), shown in graphs.

Question 13

Procedure

Answer 13

Knowledge (need to know, like programming language and code itself) -> conjecture (example : “the code is correct), which creates an equation (the middle point).

Question 14

Union

Answer 14

The union of two sets (no repetitions) - U

Question 15

Intersection

Answer 15

Appears in both sets - ∩

Question 16

Empty Set

Answer 16

Ø

Question 17

Relative Complement

Answer 17

~
A = {4,7,8}
B = {4,9,10}
A ~ B = {7,8}
Find in A, but not in B
A = {x elem Integers | x id odd}
~A = all even integers, since all odd integers is in other set x

Question 18

Symmetric Difference

Answer 18

Part of A but not B or part of B but not A (Union - Intersection)
A = [4,7,8]
B = {4,9,10}
Then = {7,8,9,10}

Question 19

Cardinality

Answer 19

The cardinality of a finite set A is the number of distinct elements in A, and is denoted by |A|.
|{1,2,5}| = 3 (number of distinct elements)
|{1,1,2,2,3}| = 3

Question 20

Set Of All Subsets

Answer 20

|Pow(A)|
|2^A| = 2^|A|