Basic Ideas of Sets

Basic Ideas of Sets

Day 1

A set is a well-defined collection of objects.

These objects are called elements or members of the set.

Multiple Choice

Which of the following sets are well defined?

• the set of all small numbers

• the set of all positive odd numbers

• the set of honest senators

• the set of tall students in your class

Multiple Choice

Set D is the set of the distinct letters in the word mathematics. Write the set using the Roster method.

• D = {m, a, t, h, e, m, a, t, i, c, s}

• D = {m, a, t, h}

• D = {m, a, t, h, e, i, c, s}

• D = {m, a, t, h, i, c, s}

Multiple Choice

Which of the following is NOT a set-builder notation for set A = {2, 4, 6, 8, 10, ...}?

• A = { x | x is a positive even number}

• A = { x | x is a positive multiple of 2}

• A = { x | x is an integer}

Multiple Choice

A set of first five odd numbers can be written as

• A = {1,2,3,5,7}

• A = {0,3,5,7,9}

• A = {1,3,5,7,9}

• A = {1,3,6,7,9}

Multiple Choice

Write the following using set builder notation.

B = {1, 4, 9, 16, 25}

• B = { x : x < 26, x is a cube number}

• B = { x : x ≤ 25, x is a square number}

Multiple Choice

The symbol for an empty set is ___.

• $\phi$

• $\theta$

• $\epsilon$

• $\ne$

Empty Set

{ }

Multiple Choice

The __________ of a set refers to the number of elements in the set.

• cardinality

• union

• intersection

• difference

Multiple Choice

Find n(A) when
A = {14, 16, 18, 20, 22, 24}

• 6
• 12
• 4
• 8

Multiple Choice

A = {t,e,n}, B = {n,e,t}

• Sets A and B are equal sets

• Sets A and B are not equal sets but are equivalent sets

• Sets A and B are not equivalent sets nor equal sets

• Sets A and B are equal sets but are not equivalent sets

Equal Sets

Two sets that contain exactly the same elements

Multiple Choice

What is TRUE regarding the following sets?

C = {m,a,t,h}, D = {g,e,o,m}

• Sets C and D are equal sets

• Sets C and D are not equal sets but are equivalent sets

• Sets C and D are not equivalent sets nor equal sets

• Sets C and D are equal sets but are not equivalent sets

Equivalent Sets

Two sets that contain exactly the same number of elements

Multiple Choice

True or false? {1,2,3,4} is subset from {1,2,3,4,5,6,7,8,9}

• True

• False

Subset

Set A is a subset of Set B if and only if every element in A is also an element in B.

Every set is a subset of itself.

An empty set is a subset of every set.

Multiple Choice

True or false? {R,G,B} is a proper subset from {R,G,B}.

• True

• False

Proper Subset

Set A is a proper subset of Set B if and only if there is at least one element in B not contained in A.

Multiple Choice

Which of the following symbols mean proper subset?

•  $\subset$  

•  $\subseteq$  

•  $\in$  

• =

Multiple Choice

If

U (the universal set) = {1, 3, 5, 7, 9, 11, 13, 15, 17} and W = {5, 7, 9, 11}, then W' = . . ..

• {1, 3, 13, 15, 17}

• {1, 3}

• {2, 4, 6, 8, 10, 12, 14, 16}

• {1, 3, 5, 7, 9, 11, 13, 15, 17}

The COMPLEMENT of set A, written as A',

contains all the elements in the universal set U that is not in set A.

Multiple Choice

Given: U = {1,2,3,4,5}, and A = {1,3,5} Find: A'

• A' = {2,4}

• A' = {1,3}

• A' = {1,5}

• A' = U

Multiple Choice

Given: A = {a,e,i,o,u}, and B = {a,b,c,d,e} Find: $A\cup B$  

•  $A\cup B=\left\{a,e,i,o,u,c,b\right\}$  

•  $A\cup B=\ \left\{a,b,c,d,e,u\right\}$  

•  $A\cup B=\left\{a,e,i,o,u\right\}$  

•  $A\cup B=\left\{a,e,i,o,u,b,c,d\right\}$  

The UNION of sets A and B,

written as A U B, is the set containing all elements that are in A and B.

Multiple Choice

What is the symbol for union of set?

• ∩

• U

• { }

• ∅

Multiple Choice

If A = {1,2,3}, B = {3,4,5}, C = {5,6,7}, find A U B U C.

• {1,2,3,4,5,6,7}

• {1,2,3,4,5,6,7,8}

• {1,2,3,3,4,5,5,6,7}

• {3,4,5}

Multiple Choice

Given: A = {1,2,3,4,5,6}, B = {2,4,6} and C = {1,3,5} Find:  $A\cap B$  

•  $A\cap B=\left\{2,4,6\right\}$  

•  $A\cup B\ =\ \left\{2,4,6\right\}$  

•  $A\cap B\ =\left\{1,3,5\right\}$  

•  $A\subset B=\left\{1,3,5\right\}$  

The INTERSECTION of sets A and B,

written as A ∩ B, is the set of elements that are members of both A and B.

Multiple Choice

What is the symbol for intersection of set?

• ∩

• U

• { }

• ∅

Multiple Choice

If A= {10,20,30,40},B={20,40,60} and C = {10,20,40,60,80}, find A Ո B Ո C

• {20,40}

• {20,40,60}

• {10,20,30,40,50,60,80}

• {10,20,30,...}

Multiple Choice

Given: A = {r,o,y,g,b,i,v} and B = {r,y,b} Find: A - B

• A - B = {g,i,v}

• A - B = { }

• A - B = {o,g,i,v}

• A - B = {r,y,b}

The DIFFERENCE of sets A and B,

written as A - B, is the set of elements in A that are not in B.

Multiple Choice

Given: A = {r,o,y,g,b,i,v} and B = {r,y,b} Find: B - A

• A - B = { }

• A - B = {r,y,b}

• A - B = {o,g,i,v}

• A - B = {g,i,v}

Multiple Choice

Given:

U = { 1, 2, 3, 4, 5}

A = { 1, 2, 3 }

B = { 1, 3, 4 }

What is the (AUB)' ?

• ( A U B )’ = {1,2,3,4}

• ( A U B )’ = {1,2}

• ( A U B )’ = {3,4}

• ( A U B )’ = {5}