Math 1332 – Sample Test 1
1. Write each set using the roster method
a. The set of natural numbers greater than 5 and less than 12.
Answer. { 6 , 7 , 8 , 9 , 10 , 11 }
b. The set of names of three latest US presidents.
Answer. { Bill Clinton, George W. Bush, Barack Obama }
c. The set of number of months in a year.
Answer. { 12 }
2. Determine whether each of the following statements are true or false (circle the correct answer)
a. 3 ∈ { 2, 4 , 5 , 8 }
T
F
b. 7 ∈ { x | x ∈ N and 2 < x < 10 }
T
F
c. Monday ∈ { x | x is a day in a week }
T
F
3. Find the cardinal number for the following sets
a. A = { a , d , e , g , h }
Answer. n ( A ) = 5
b. B = { x | x ∈ N AND 7 < x ≤ 13 }
Answer. n ( B ) = 6
c. C = { x | x is a continent }
Answer. n ( C ) = 7 ( or 6 )
4. Given
U = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 }
A = { 1 , 2 , 3 , 4 , 5 , 6}
B = {5,6,7,8,9}
C = { 3 , 4 , 7 , 9 , 10}
Find the following subsets
a. B’
Answer. B’ = { 1 , 2 , 3 , 4 , 10 , 11 , 12 }
b. A  B
Answer. A  B = { 5 ,6 }
c. B U C
Answer. B U C = { 3 ,4 , 5 , 6 , 7 , 8 , 9 , 10}
d. A’  ( B U C ’ )
Answer. C ‘ = { 1 , 2 , 5 , 6 , 8 , 11 , 12 }
B U C ’ = { 1 , 2 , 5 , 6 , 7 , 8 , 9 , 11 , 12 }
A ‘ = { 7 , 8 , 9 , 10 , 11 , 12 }
A’  ( B U C ’ ) = { 7 , 8 , 9 , 11 , 12 }
5. Given the Venn diagram below.
Verbally state the following regions
a. { III }
Answer. Reading but not Math nor Physics
b. { II }
Answer. Reading and Math but not Physics
c. { V }
Answer. Reading and Math and Physics
6.
Answer: 69
Math
36
31
English
64
69
7. Write the negation of the following statements
a. I go home and I do not study.
Answer: Either I do not go home or I study.
b. There are mosquitoes that do not carry diseases. ( using an universal quantifier )
Answer: All mosquitoes carry diseases.
c. All of these medicines are effective. ( using an existential quantifier )
Answer: Some of these medicines are not effective.
8. Let p = “The kid played outside” , q = “It was sunny” , and r = “The kid did homework”. Write the
following statements in English.
a. p  q
Answer: The kid played outside and it was sunny.
b.  r  p
Answer: Either the kid did not do homework or the kid played outside .
c. q  r  p
Answer: If it was sunny and the kid did homework , then the kid played outside .
9. Let p = “She is taking an English course” and q = “She is taking a Math course”. Write the
following statements in symbols.
a. She is taking an English course but not a Math course.
Answer. p   q
b. If she is taking a Math course then she is not taking an English course.
Answer. q   p
c. She is taking neither an English course nor a Math course.
Answer.  q   p
10. Construct a truth table for the following symbolic statements
a. p   q
p
q
q
pq
T
T
F
T
T
F
T
T
F
T
F
F
F
F
T
T
b. p  q  p
p
q
pq
pqp
T
T
T
T
T
F
F
T
F
T
F
T
F
F
F
T
c. p  (  q  r )
p
q
r
q
qr
p(qr)
T
T
T
F
T
T
T
T
F
F
T
T
T
F
T
T
T
T
T
F
F
T
F
T
F
T
T
F
T
T
F
T
F
F
T
T
F
F
T
T
T
T
F
F
F
T
F
F