Chapter 2 – Sets

Terminology Element, member

Roster Method: A = {2,4,6,8,10}

Rule Method: {x|x is a student enrolled in T101 this semester}

Natural Numbers or Counting Numbers N = {1, 2, 3, 4, …}

Set Builder Notation {x| x is a even numbers between 3 and 12}

Equal Sets

B = {r, s, t} C = {t, s, r} {r, m} = {m, r}

Cardinality The number of elements in a set is its cardinality

n(A) = n(B) =

n({p, q, r, s, t, u})

Null Set, Empty set

{ } or but NOT {}

n() = 0 That is: the cardinality of the null set is zero

Complement Need to define a universal set

U = {1, 2, 3, 4, …, 10} B = {1, 3, 6, 7, 8, 10}

Find and find n(B), n(), n(U),

If U = {m, i, c, h, a, e, l}

K = {i, c, e} find its complement

T = {h, e, l} find the complement

E = { } find the complement

R = {m, i, c, h, a, e, l} find the complement

Subset

A is a subset of B if every element of A is an element of B

A is a proper subset of B if every element of A is an element of B AND

R = {p, q, r, s, m}

True or False: {p, q, m} R {p, q, m} R

{p, q, m} {p, q, m} {p, q, m} {p, q, m}

If A = {2, 4, 6, 8, 10) B = {4, 8} C + {2, 3, 4}

True or False: B A C A B B B B

Set Intersection

U = {a, b, c, e, f, h, I, l, m, n, t, w}

A = {m, i, c, h, a, e, l} and B = {m, a, t, h, e, w}

Find:

Set Union

Find:

Set Difference

Find: A = B B = A

Disjoint Sets

Examples:

U = {m, a, t, h, e, I, c, s} A = {m, a, t, h} B = {h, a, t}

C = {t, h, e } D = {t, h, e, m } E = {t, h, I, s} F = {m, i, c, e}

G = {i, c, e }

Find any disjoint sets in the list of sets above.

Do several versions