Subset of a Set

1.    Determine the subset of a set and the number of subsets of a given set.

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2.    Find the powerset of any given set.

​​Subset of a set.

​Objectives

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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}

Multiple Choice

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

• 11

• 8

• 6

• 4

Multiple Choice

Which of the following is the symbol of an empty set?

• $$\cap$$

• $$\cup$$

• $$\subseteq$$

• $$\phi$$

Multiple Choice

Write the given set B = {x/x is an odd number between 11 and 20} in roster form.

• B = {11, 13, 15, 17, 19}

• B = {13, 15, 17, 19}

• B = {12, 13, 14, 15, 16, 17, 18, 19}

• B = {11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

Multiple Choice

Which of the following set has the cardinality equals to 5?

• Set A is the set of counting numbers less than 5

• Set B is the set of letters in the word "RACER"

• Set C is the set of positive multiples of 5

• Set D is a set of vowels in the English Alphabet

Multiple Choice

Which one of the following sets is infinite?

• The set of whole numbers less than 10

• The set of numbers between 10 and 20

• The set of factors of 10

• The set of integers greater than 10

Multiple Choice

Set C is the set of factors of 18.

Which of the following is NOT an element of set C?

• 2

• 3

• 5

• 9

Multiple Choice

An object or member in a set is called __________.

• an element

• an item

• a person

• a thing

Multiple Choice

If D = {m/m is a positive even integer less than 13}, then

• D = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

• D = {1,3, 5, 7, 9, 11}

• D = {2, 4, 6, 8, 10, 12}

• D = {0, 2, 4, 6, 8, 10,}

Multiple Choice

Which of the following best describes set P, where P = {car, tricycle, train, airplane, boat}

• {types of public transportation}

• {name of places most visited}

• {four things in the country}

• None of the above

Multiple Choice

If two sets are equal, they are also equivalent.

• True

• False

Multiple Choice

E = {0} represents a null set.

• True

• False

Multiple Choice

It is a method of writing sets by using a descriptor

• Roster form

• Set-builder form

• Algebraic form

• Universal form

Multiple Choice

It is the set that contains all objects under consideration.

• Elements

• Universal Set

• Subset

• Proper Subset

Multiple Choice

Jennifer listed the set of all letters in the word "library" as shown below. What is WRONG with this set?

A = {l, i, b, r, a, r, y}

• A capital letter is used to represent this set.

• It uses commas.

• It uses braces.

• The objects in this set are not unique.

Multiple Choice

What is the punctuation use to enclose the given set?

• Parenthesis

• Bracket

• Braces

• None of the above

Multiple Choice

What is the correct verbal description of set E = {p, h, i, l, n, e, s}

• Set E is the set of consonants in the word "Philippines"

• Set E is the set of letters in the word "Philippines"

• Set E is the set of vowels in the word "Philippines"

• All of the above.

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

Which of the following is considered as joint set of set G = {a/a is a counting numbers}?

• {-2, -1, 0}

• $$\left\{\frac{1}{4},\ \frac{1}{2},\ \frac{3}{4}\right\}$$

• {1.25, 1.5, 1.75}

• {1, 2, 3, 4, 5}

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 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.

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 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.

Subset of a set.

Examples: List all the subsets of the given set.

1.   J = { 5 }

the number of subset is,  ​

Subset of a set.

Subset of a set.

Subset of a set.

Subset of a set.

Subset of a set.

Subset of a set.

Examples: List all the subsets of the given set.

2.   A = {pink, purple}

the number of subset is,  ​

Subset of a set.

Subset of a set.

Subset of a set.

Subset of a set.

Subset of a set.

Subset of a set.

Examples: List all the subsets of the given set.

2.   M = {a, b, c}

the number of subset is, ​

Subset of a set.

Subset of a set.

Subset of a set.

Subset of a set.

Subset of a set.

Examples: List all the subsets of the given set.

2.   J = { }

the number of subset is,  ​

Subset of a set.

Subset of a set.

Subset of a set.

Subset of a set.

Subset of a set.

Subset of a set.

End of discussion.​