Sets

Question 1

Set notation

Answer 1

A = { x ⱻ S | P(x) } the objects in set S where P(x) is true

Question 2

Natural numbers

Answer 2

ℕ - {0,1,2,3,4,…}

Question 3

Integers

Answer 3

ℤ - {…,-2,-1,0,1,2,3,…}
ℤ+ - {0,1,2,3,…}

Question 4

rational numbers

Answer 4

Q - {x/y | x ⱻ ℤ, y ⱻ ℤ, y /= 0 }
any number that can be written as a fraction with an integer numerator and denominator

Question 5

Real Numbers

Answer 5

anything that doesn’t have an i in it

Question 6

the characteristic vector of [1,2,3,4,5] under A = {1,3,5}

Answer 6

[1,0,1,0,1]

Question 7

Sub Set

Answer 7

A set is called a subset of another if every element is also an element of another set
denoted by B ⊆ A where B is a subset of A

Question 8

Equal Sets

Answer 8

two sets are equal if B ⊆ A and A ⊆ B

Question 9

Union

Answer 9

same as OR

Question 10

Intersection

Answer 10

Same as AND

Question 11

relative complement

Answer 11

A - B
All values that exist in A but not in B

Question 12

Complement

Answer 12

~A = {x| x ∄ A}

Question 13

Symmetric Difference

Answer 13

All values that are unique to both A and B
A Δ B = {x | (x ⱻ A and x ∄ B) or (x ⱻ B and x ∄ A)}

Question 14

Commutative Law

Answer 14

union and Intersection are both commutative

Question 15

Associative Law

Answer 15

A U (BUC) = (A U B ) U C
A n (B n C) = (A n B) n C

Question 16

Distributive Law

Answer 16

A U ( B n C) = (A nB ) u A( n C)