Voacbulario

Laboratory: The Real Numbers
By Lic. Mario A. Cantú Montemayor and Ing.Ma.Alejandra Ruiz Borges

Name_________________________________________I.D. Number:______________ Group: _______

Read the following guidelines carefully.
* Due day: August 28th 2012 in class
* No late work will be accepted.
* Place your name, ID number, and group number in the header of the lab.
*Solve the following problems showing full and comprehendible procedures, in a neat and orderly manner.
* Attach sheets on which you show all the needed procedures.
* Clearly number the problem you are solving, and underline or box the final answer.
* Staple your procedure sheets in the correct order. Instructions: Solve the following exercises. Remember that is very important toshow a complete and ordered procedure, and also it´s important to use proper math notation.


1. Determine if the following numbers are rational or irrational.
___
a) 3.875 d) 0.251

b) e) 0.1524336717…

c) f) -3.014

2. For the following numbers, determine all the subsets of thereal numbers that they belong:
a) d) -3.2543125440……

b) 13 / 21 e) 4

c) f)

3. Answer True or Flase to the following propositions:
a. ( ) Z+ - N = { }
b. ( ) R - Q = QC
c. ( ) ∀x ∈Q, x ∈R
d. ( ) Z N
e. ( ) 84 is divisible by 3
f. ( ) The number 0.4444444444…..is a rational number
g. ( ) The number 4.212112111211112…. is a rational number
h. ( ) Q R
i. ( ) 7 ∈ Q
j. ( ) π ∉ R
k. ( ) { 3 } ∈ { 1, 2, 3 }
l. ( ) 3 ⊂ { 1, 2, 3 }

4. Write the following numbes as prime factors:
a) 48 =c) 500 =

b) 51 = d) 1001 =

5. Find the Greatest Common Factor (GCF) form the following numbers:
a) 8 y 12 = c) 15, 10 y 75 =

b) 30 , 40 y 60 = d) 12 y 17 =

6. Find the Least Common Multiple (LCM) from the following numbers:
a) 14 y 10 = c) 20,30 y 90 =

b) 3, 6 y 12 = d) 56 y 154 =

Laboratory: Sets and Venn Diagrams
by Lic. Mario A. Cantú Montemayor and Ing.Ma.Alejandra Ruiz Borges
* Staple your procedure sheets in the correct order. Instructions: Solve the following exercises. Remember that is very important to show a complete and ordered procedure, and also it´s important to use proper mathnotation.


1. Write each set by enumeration (or roster form) and determine its cardinality.

A = { x|x is an odd digit } | | n(A) = |
B = {x /x ∈ N,−5 < x ≤ 9} | | n(B) = |
C = {x/x ∈ Z+,−5 < x ≤ 3} | | n(C) = |

2. Write each set by comprehension (or description) and determine its cardinality.

B = { 11, 13, 17,19,23,29,31 } | | n(B) = |
C = { 0,1,2,3,4,5… }| | n(C) = |
D = { Mercury, Venus, Earth, Marts, Jupiter, Saturn, Uranus, Neptune } | | n(D)= |

3. Considering the following sets:
U = {x ∈ Z / -4 < x < 12 }
M = { x∈ Z/5 < x < 10}
N = {x ∈ Z+/- 2 ≤ x ≤ 11}
P = {x ∈ N /8 < x ≤ 10}

Find the set that results from each of the following operations:
a) P M ´

b) N´ (M P)

c) (M N)´ P

d) [ P -(N M)] – ( MC - P )

4. Determine if the following propositions are True or False:
a) ∃ x ∈ N, x2 -1 < 0

b) ∃ x ∈ R , x2 -1 < 0

c) ∀x ∈ R, x ∈Q

d) ∀x ∈W, x ∈R

5. Show on the diagrams provided, the result of the indicated operations. You may use the back of the page to show procedures.

a) d)
U N...