Kylie - lesson on Sets

SET

is a well-defined group of objects

Multiple Choice

Which of the following is a well-defined set?

• The beautiful teachers of Grade 7.

• All difficult questions in the chapter test.

• The cast in the series Stranger Things.

• The tall students in Manila Science High School

Multiple Choice

Set A is the letters in the name " jennylyn"

• A = {j,e,n,n,y,l,y,n}

• A = {j,e,n,y,l,y,n}

• A = {j,e,n,y,l}

• A = {j.e.n}

Element of a Set

An object or idea in a set is called an element (or member) of the set. Notation: The symbol ∈ is used to denote that an element is a member of a set and ∉ is used to denote that an object is not a member of a set.

Multiple Choice

Given the set of letters in the word "mathematics", what is the cardinality of the given set?

• 11

• 8

• 6

• 4

SUBSET

A subset is a set whose elements are all members of another set. The symbol "⊆" means "is a subset of". The symbol "⊂" means "is a proper subset of".

Subset of a set

​Ø A set is a subset of another set if all elements of the former are also the elements of the latter. Subset is denoted by the symbol (Í ).

• A part of a larger group of related things

Subset of a set.

Given:

A = {1, 3, 5, 7, 9}  F = {8, 6, 4, 2} 

B = {red, yellow, blue}       G = {1, 2, 3, 4, 5}

C = {x/x is a letter of the English Alphabet}    H = {1, 2, 3, 1, 2}

D = {a/a is a counting numbers}  I = {m/m is a primary color}

E = {2, 4, 6, 8}  J = {  }

Ø If there is at least one element found in set B but not found in set A, or if set B has more elements than set A but all elements of set A are also elements of set B, then set A is a proper subset of set B, denoted by ( A Ì B ).

Example: A Ì D   D Ë A

H Ì G   G Ë H​

Subset of a set.

Given:

A = {1, 3, 5, 7, 9}  F = {8, 6, 4, 2} 

B = {red, yellow, blue}       G = {1, 2, 3, 4, 5}

C = {x/x is a letter of the English Alphabet}    H = {1, 2, 3, 1, 2}

D = {a/a is a counting numbers}  I = {m/m is a primary color}

E = {2, 4, 6, 8}  J = {  }

​Ø Set A is an improper subset ( Í ) of set B if every element of A belongs to B, or if set A and set B are equal sets. In symbol, A  Í  B  if  x Î A, then x Î B.

Example:  B Í I I Í B

E Í F F Í E​

Subset of a set.

Null or Empty Set

is the set that does not contain anything. It is symbolized or { }.

Given:

A = {1, 3, 5, 7, 9}  F = {8, 6, 4, 2} 

B = {red, yellow, blue}       G = {1, 2, 3, 4, 5}

C = {x/x is a letter of the English Alphabet}    H = {1, 2, 3, 1, 2}

D = {a/a is a counting numbers}  I = {m/m is a primary color}

E = {2, 4, 6, 8}  J = {  }

Ø An empty set is always a subset of any or every set.

​ Example: J Ì C

​Ø Every set is a subset of itself.

​ Example: A Í B​

Subset of a set.

Multiple Choice

This is the term used when we want to determine the number of elements on a given set.

• Counting Sets

• Listing

• Cardinality

• Power set

Multiple Choice

If U = {1, 3, 5, 7, 9, 11, 13}, then which of the following are subsets of U.

• C = {1, 9, 5, 13}

• F = {2, 3, 4, 5}

Multiple Choice

An object or member in a set is called __________.

• an element

• an item

• a person

• a thing

Multiple Choice

What is the punctuation use to enclose the given set?

• Parenthesis

• Bracket

• Braces

• None of the above