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Lecture 7

Definitions:

= Object:  Person, Place or Thing<= /span>

= Set: A collection of objects.

= Elements:  The objects contained within a set= .

= { } are called braces. 

,  is called a comma.

<= /span> is called Epsilon (a Greek letter)

<= span style=3D'font-size:11.0pt;line-height:115%;font-family:"Calibri","sans-seri= f"; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareas= t-theme-font: minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:"Times Ne= w Roman"; mso-bidi-theme-font:minor-bidi;position:relative;top:4.5pt;mso-text-raise:-= 4.5pt; mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'= ><= /span> “An element of”<= span style=3D'font-family:"Times New Roman","serif"'>

= A set is often displayed by writing a list of its elements separated by commas betwe= en braces. 

= For instance:

= {J, A, M, E, S} is a set containing the letters of my name.  Elements of sets are usually liste= d in alphabetical order. 

= Hence,

= {J, A, M, E, S} =3D {A, E, J, M, S}

= Note: A <= /span> {J, A, M, E, S}

= For instance:

{ 2, 0, 6= , 3, 2, 5, 3, 1, 1, 9} is a set containing the digits of a phone number.  Like Elements of a set are usually listed only once.   Numbers are frequently listed in ascending order.

= Hence,

{ 2, 0, 6= , 3, 2, 5, 3, 1, 1, 9 } =3D { 0, 1, 2, 3, 5, 6, 9 }

= Note:  6 <= /span> { 0, 1, 2, 3, 5, 6, 9 }

Definitions:

= Natural Numbers:  The set of numbers obtained by sta= rting at 1 and summing 1 to the number. 
{ 1, 2, 3, 4, … }

= Whole Numbers:  The set of numbers obtained by sta= rting at 0 and summing 1 to the number. 
{ 0, 1, 2, 3, 4, … }

= Integer Numbers:  The set of numbers obtained by starting at -1 and summing -1 to the number and the set of Natu= ral Numbers.
{  …= , -4, -3, -2, -1, 0, 1, 2, 3, 4, … }

 

Objectives:

·         To recognize and correctly identify the elements of the sets of Whole Numbers, Counting Numbers, and Integer Numbers.  

·         To recognize and properly use the set notation and the “element” symbol..

Examples:

1.&n= bsp;      Indicate the truth value of the statement. <= /p>

a.&n= bsp;      -2 is a Natural Number.            =      FALSE

b.&n= bsp;     - 2 is a Whole Number.            =       FALSE

c.&n= bsp;      - 2 is an Integer Number.            =   TRUE

 

2.&n= bsp;      Indicate the truth value of the statement. <= /p>

a.&n= bsp;      9 is a Natural Number.            =        TRUE

b.&n= bsp;     9 is a Whole Number.            =          TRUE

c.&n= bsp;      9 is an Integer Number.            =             &nb= sp;       TRUE

 

 

3.&n= bsp;      Indicate the truth value of the statement. <= /p>

a.&n= bsp;      -1, 001 is a Natural Number.        &= nbsp;           &nbs= p;   FALSE

b.&n= bsp;     -1, 001 is a Whole Number.        &= nbsp;           &nbs= p;     FALSE

c.&n= bsp;      -1, 001 is an Integer Number.        &= nbsp;            TRUE



4.&n= bsp;      Indicate the truth value of the statement. <= /p>

a.&n= bsp;      a  <= /span>   { b, c, d }        &= nbsp;                   &= nbsp;           &nbs= p;           FALSE=

b.&n= bsp;     a  <= /span>   { 1, 2, 5 }            =                  &= nbsp;           &nbs= p;           FALSE=

c.&n= bsp;      a  <= /span>   { a, b, c, d }        &= nbsp;               &= nbsp;           &nbs= p;           TRUE<= br>

5.&n= bsp;      Indicate the truth value of the statement. <= /p>

a.&n= bsp;      cat  <= /span><= /span>   { cat, dog, horse }        &= nbsp;           &nbs= p;          TRUE

b.&n= bsp;     -3   <= /span>   { 1, 2, 5 }            =               &= nbsp;           &nbs= p;           FALSE=

c.&n= bsp;      -3   <= /span>   { -3, -2, -1, 0, 1, 2, 3 }        &= nbsp;         &= nbsp;       TRUE

 

 

 

Exercises:

1.&n= bsp;      Indicate the truth value of the statement. <= /p>

a.&n= bsp;      -7 is a Natural Number.            =     

b.&n= bsp;     - 50 is a Whole Number.            =             &nb= sp;      

c.&n= bsp;      - 225 is an Integer Number.         =

 

2.&n= bsp;      Indicate the truth value of the statement. <= /p>

a.&n= bsp;      7 is a Natural Number.            =       

b.&n= bsp;     7 is a Whole Number.            =         

c.&n= bsp;      7 is an Integer Number.            =             &= nbsp;      

 

 

3.&n= bsp;      Indicate the truth value of the statement. <= /p>

a.&n= bsp;      -10, 500 is a Natural Number.        &= nbsp;           &nbs= p;

b.&n= bsp;     -10, 500 is a Whole Number.        &= nbsp;           &nbs= p; 

c.&n= bsp;      -10, 500 is an Integer Number.        &= nbsp;         



4.&n= bsp;      Indicate the truth value of the statement. <= /p>

a.&n= bsp;      a  <= /span>   {  c, d, e }            =             &nb= sp;            =             &nb= sp;

b.&n= bsp;     a  <= /span>   { 11, 12, 15 }        &= nbsp;             &= nbsp;           &nbs= p;          

c.&n= bsp;      a  <= /span>   { a, b, c, d, e }        &= nbsp;          &= nbsp;           &nbs= p;          


5.&n= bsp;      Indicate the truth value of the statement. <= /p>

a.&n= bsp;      dog  <= /span><= /span>   { cat, dog, horse }        &= nbsp;           &nbs= p;       

b.&n= bsp;     -3   <= /span>   { 1, 2, 15 }        &= nbsp;               &= nbsp;           &nbs= p;          

c.&n= bsp;      -3   <= /span>   { -3, -2, -1,  2, 3 }           &= nbsp;               &= nbsp;      

 

 

6.&n= bsp;      Indicate the truth value of the statement. <= /p>

a.&n= bsp;      x  <= /span>   { a, x, u, z  }&= nbsp;           &nbs= p;          &= nbsp;           &nbs= p;          

b.&n= bsp;     3   <= /span>   { 1, 2, 15 } &n= bsp;            = ;            &n= bsp;     

c.&n= bsp;      3   <= /span>   { -3, -2, -1,  2, 3 }            &= nbsp;           &nbs= p;          


 

Solutions:

1.&n= bsp;      Indicate the truth value of the statement. <= /p>

a.&n= bsp;      -7 is a Natural Number.            =      FALSE

b.&n= bsp;     - 50 is a Whole Number.            =             &nb= sp;       FALSE

c.&n= bsp;      - 225 is an Integer Number.         = TRUE

 

2.&n= bsp;      Indicate the truth value of the statement. <= /p>

a.&n= bsp;      7 is a Natural Number.            =        TRUE

b.&n= bsp;     7 is a Whole Number.            =          TRUE

c.&n= bsp;      7 is an Integer Number.            =             &nb= sp;       TRUE

 

 

3.&n= bsp;      Indicate the truth value of the statement. <= /p>

a.&n= bsp;      -10, 500 is a Natural Number.        &= nbsp;           &nbs= p; FALSE

b.&n= bsp;     -10, 500 is a Whole Number.        &= nbsp;           &nbs= p;  FALSE

c.&n= bsp;      -10, 500 is an Integer Number.        &= nbsp;          TRUE



4.&n= bsp;      Indicate the truth value of the statement. <= /p>

a.&n= bsp;      a  <= /span>   {  c, d, e }            =             &nb= sp;            =             &nb= sp; FALSE

b.&n= bsp;     a  <= /span>   { 11, 12, 15 }        &= nbsp;             &= nbsp;           &nbs= p;           FALSE=

c.&n= bsp;      a  <= /span>   { a, b, c, d, e }        &= nbsp;          &= nbsp;           &nbs= p;           TRUE<= br>

5.&n= bsp;      Indicate the truth value of the statement. <= /p>

a.&n= bsp;      dog  <= /span><= /span>   { cat, dog, horse }        &= nbsp;           &nbs= p;        TRUE

b.&n= bsp;     -3   <= /span>   { 1, 2, 15 }        &= nbsp;               &= nbsp;           &nbs= p;           FALSE=

c.&n= bsp;      -3   <= /span>   { -3, -2, -1,  2, 3 }           &= nbsp;           &nbs= p;           TRUE<= /p>

 

6.&n= bsp;      Indicate the truth value of the statement. <= /p>

a.&n= bsp;      x  <= /span>   { a, x, u, z  }&= nbsp;           &nbs= p;          &= nbsp;           &nbs= p;           TRUE<= /p>

b.&n= bsp;     3   <= /span>   { 1, 2, 15 } &n= bsp;            = ;            &n= bsp;      FALSE

c.&n= bsp;      3   <= /span>   { -3, -2, -1,  2, 3 }            &= nbsp;           &nbs= p;           TRUE<= /p>

 

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