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Finite
Math
Week 1 Quiz – Logic & Sets
MULTIPLE CHOICE SECTION
For each section, read the instructions and choose the best answer.
1. Which of the following is a statement?
a)
What is your favorite movie?
b)
Study hard for this class.
c)
Topeka is the capital of Kansas.
d)
The Gibson SG is the coolest guitar.
2. Which of the following is a statement? a)
Pepperoni is the tastiest pizza topping. b) Do you come to Milwaukee often?
c)
Consider each sentence carefully.
d)
Monotremes are mammals that lay eggs.
Identify the symbolic expression that best represents the following compound statements. The statement
variables are defined as follows:
p:
It is Friday.
q:
Bridget is going shopping.
r:
It is payday.
(
Versio
n
B
)
3. If it is Friday, then Bridget is going shopping.
a)
p →q
b)
p ∨ q
c)
q → p d)
p ↔ q
5. It is payday if and only if it is Friday and Bridget
is going shopping.
a) ¬p ∨ ¬q ∧ r
b)
r →q
c)
r ↔ ( p ∧ q)
d)
p →(q ∧ r)
4. It is Friday and it is not payday.
a)
p ∨ r
b)
p →¬r
c)
p ∧ ¬r
d)
p ⊕ r
6. If it is not payday, then Bridget is not going
shopping. a) ¬r ↔ q
b) ¬r →¬q
c) ¬r ∧ ¬q
d) ¬q ⊕ r
Given the following truth-‐values for some statements p, q, and r; determine the truth-‐value of the following statements.
p:
TRUE. q: FALSE. r: TRUE.
(
Finite
Math
Week
1
Quiz
–
Logic
&
Sets
)
(
Version
B
)
7. ¬q → r
a) True
b) False
9.
p →(q ∨ r)
a) True
b) False
8. (q ∨ r) ↔ ( p ∨ q)
a) True
b) False
10. ¬( p ∧ r) ∨ q
a) True
b) False
Determine which statement is logically equivalent to the given statement.
11. ¬( p ∧ q) ≡
a) ¬p →¬q
b) ¬p ∨ ¬q
c) ¬p ∧ ¬q
d) Contradiction (F)
12.
p ∨ (q ∧ r) ≡
a) ¬p →¬q
b)
p ∧ r ∧ q
c) ( p ∨ q) ∧ ( p ∨ r)
d) Tautology (T)
13. (q ∧ ¬q) ≡
a) ¬p →¬q
b)
q
c) ¬p ∧ ¬q
d) Contradiction (F)
Given the following set:
A = {Druid, Hunter, Mage, Paladin,Pr iest, Rogue, Shaman,Warlock,Warrior, DeathKnight}
Determine if the following set relations are true or false.
14. {Hunter, Rogue} ⊆ A
a) True
b) False
15.
DeathKnight ∉ A
a) True
b) False
16.
{Pr iest, Shaman,Warlock,Warrior} ⊄ A
17.
A ⊆ ∅
a) True
b) False
a) True
b) False
For the following universal set:
U = {0,1,2, 3, 4,5,6, 7,8,9,10,11,12,13,14,15}
Given the following sets:
R = {2, 3,5, 7,11,13}
S = {0,2, 4,6,8,10,12,14}
T = {1,2, 3, 4,5}
Identify the set of elements described by the following set relationships.
18.
S ∪ (R ∩ T )
a) {0,1,2, 4,5,6,8,10}
b) {0,2, 3, 4,5,6,8,10,12,14}
c) {0,2, 4,6,8,10,12,14}
d) None of the Above
(
c
)20. (S ∪ T )
19.
R \ T
a) {7,11,13} b) {3, 4,5,11} c) {0, 3, 7,13}
d) None of the Above
(
c
)21.
S ∪ (Rc ∩ T )
a) {7,9,11,13,15}
b) {0,1, 3, 7,9,10,11,12}
c) {0,1, 3,5,6, 7,8,9,10,11,12,13,14,15}
d) None of the Above
a) ∅
b)
U
c) {0,2, 3, 4,5,6, 7,8,9,10,11,12,13,14,15}
d) None of the Above
Identify the relationship depicted in the Venn Diagrams below:
22.
a)
B
b)
B \ A
c)
A ∩ B
d)
A \ B
23.
a) ( A ∩ B)c
b)
U
c)
U \ ( A ∩ B)
d) ( A ∪ B)c
24.Describe the following set using set builder notation:
A = {5,15,25, 35, 45,55,65}
a)
A = {x | 5 ≤ x ≤ 65}
b)
A = {x + 5 | 0 ≤ x ≤ 60} c)
A = {10 x + 5 | 0 ≤ x ≤ 6} d)
A = {5 x |1 ≤ x ≤ 13}
25. List the power set
P(S) for the set
S = {A, B,C, D, F}
a)
P(S) = {∅,{A},{B},{C},{D},{F},{A, B},{A,C},{A, D},{A, F},{B,C},{B, D},{B, F},{C, D},{C, F},{D, F},
{A, B,C},{A, B, D},{A, B, F},{A,C, D},{A,C, F},{A, D, F},{B,C, D},{B,C, F},{B, D, F},{C, D, F},
{A, B,C, D},{A, B,C, F},{A,C, D, F},{A, B, D, F}{B,C, D, F},
{A, B,C, D, F}}
b)
P(S) = {∅,{A},{B},{C},{D},{F},{A, B},{A,C},{A, D},{A, F},{B,C},{B, D},{B, F},{C, D},{C, F},{D, F},
{A, B,C},{A, B, D},{A, B, F},{A,C, D},{A,C, F},{A, D, F},{B,C, D},{B,C, F},{B, D, F},{C, D, F},
{A, B,C, D, F}}
c)
P(S) = {∅,{A},{B},{C},{D},{F},{A, B,C, D, F}}
d)
P(S) = {∅,{A},{B},{C},{D},{F},{A, B},{A,C},{A, D},{A, F},{B,C},{B, D},{B, F},{C, D},{C, F},{D, F},
{B, A},{C, A},{D, A},{F, A},{C, B},{D, B},{F, B},{D,C},{F,C},{F, D},{A, B,C},{C, B, A},{B, A,C},
{C, D, F},{F, D,C},{A, B,C, D, F}}
Finite
Math
Week
1
Quiz
–
Logic
&
Sets
Version
B
MULTIPLE
CHOICE
SECTION
For
each
section,
read
the
instructions
and
choose
the
best
answer.
1.
Which
of
the
following
is
a
statement?
a)
What
is
your
favorite
movie?
b)
Study
hard
for
this
class.
c)
Topeka
is
the
capital
of
Kansas.
d)
The
Gibson
SG
is
the
coolest
guitar.
2.
Which
of
the
following
is
a
statement?
a)
Pepperoni
is
the
tastiest
pizza
topping.
b)
Do
you
come
to
Milwaukee
often?
c)
Consider
each
sentence
carefully.
d)
Monotremes
are
mammals
that
lay
eggs.
Identify
the
symbolic
expression
that
best
represents
the
following
compound
statements.
The
statement
variables
are
defined
as
follows:
p:
It
is
Friday.
q:
Bridget
is
going
shopping.
r:
It
is
payday.
3.
If
it
is
Friday,
then
Bridget
is
going
shopping.
a)
€
p →q
b)
€
p∨
q
c)
€
q →p
d)
€
p↔ q
5.
It
is
payday
if
and
only
if
it
is
Friday
and
Bridget
is
going
shopping.
a)
€
¬p∨ ¬q∧ r
b)
€
r →q
c)
€
r ↔ (p∧q)
d)
€
p → q∧ r( )
4.
It
is
Friday
and
it
is
not
payday.
a)
€
p∨ r
b)
€
p →¬r
c)
€
p∧ ¬r
d)
€
p⊕ r
6.
If
it
is
not
payday,
then
Bridget
is
not
going
shopping.
a)
€
¬r ↔ q
b)
€
¬r →¬q
c)
€
¬r∧ ¬q
d)
€
¬q⊕ r
Finite
Math
Week
1
Quiz
–
Logic
&
Sets
Version
B
Given
the
following
truth-‐values
for
some
statements
p,
q,
and
r;
determine
the
truth-‐value
of
the
following
statements.
p:
TRUE.
q:
FALSE.
r:
TRUE.
7.
€
¬q →r
a)
True
b)
False
9.
€
p →(q∨ r)
a)
True
b)
False
8.
€
(q∨ r)↔ (p∨q)
a)
True
b)
False
10.
€
¬(p∧ r)∨q
a)
True
b)
False
Determine
which
statement
is
logically
equivalent
to
the
given
statement.
11.
€
¬ p∧q( ) ≡
a)
€
¬p →¬q
b)
€
¬p∨ ¬q
c)
€
¬p∧ ¬q
d)
Contradiction
(F)
12.
€
p∨(q∧ r) ≡
a)
€
¬p →¬q
b)
€
p∧ r∧q
c)
€
(p∨q)∧(p∨ r)
d)
Tautology
(T)
13.
€
(q∧ ¬q) ≡
a)
€
¬p →¬q
b)
€
q
c)
€
¬p∧ ¬q
d)
Contradiction
(F)
Finite
Math
Week
1
Quiz
–
Logic
&
Sets
Version
B
Given
the
following
set:
€
A = Druid,Hunter,Mage,Paladin,Priest,Rogue,Shaman,Warlock,Warrior,DeathKnight{ }
Determine
if
the
following
set
relations
are
true
or
false.
14.
€
{Hunter,Rogue}⊆ A
a)
True
b)
False
16.
€
Priest,Shaman,Warlock,Warrior{ } ⊄ A
a)
True
b)
False
15.
€
DeathKnight ∉ A
a)
True
b)
False
17.
€
A ⊆ ∅
a)
True
b)
False
For
the
following
universal
set:
€
U = 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15{ }
Given
the
following
sets:
€
R = 2,3,5,7,11,13{ }
S = 0,2,4,6,8,10,12,14{ }
T = 1,2,3,4,5{ }
Identify
the
set
of
elements
described
by
the
following
set
relationships.
18.
€
S ∪ R∩T( )
a)
€
0,1,2,4,5,6,8,10{ }
b)
€
0,2,3,4,5,6,8,10,12,14{ }
c)
€
0,2,4,6,8,10,12,14{ }
d)
None
of
the
Above
20.
€
S ∪T( )c
a)
€
7,9,11,13,15{ }
b)
€
0,1,3,7,9,10,11,12{ }
c)
€
0,1,3,5,6,7,8,9,10,11,12,13,14,15{ }
d)
None
of
the
Above
19.
€
R \T
a)
€
7,11,13{ }
b)
€
3,4,5,11{ }
c)
€
0,3,7,13{ }
d)
None
of
the
Above
21.
€
S ∪ Rc ∩T( )
c
a)
€
∅
b)
€
U
c)
€
0,2,3,4,5,6,7,8,9,10,11,12,13,14,15{ }
d)
None
of
the
Above
Finite
Math
Week
1
Quiz
–
Logic
&
Sets
Version
B
Identify
the
relationship
depicted
in
the
Venn
Diagrams
below:
22.
a)
€
B
b)
€
B \ A
c)
€
A∩ B
d)
€
A \ B
23.
a)
€
(A∩ B)c
b)
€
U
c)
€
U \ (A∩ B)
d)
€
(A∪ B)c
Finite
Math
Week
1
Quiz
–
Logic
&
Sets
Version
B
24.Describe
the
following
set
using
set
builder
notation:
€
A = 5,15,25,35,45,55,65{ }
a)
€
A = x |5 ≤ x ≤ 65{ }
b)
€
A = x + 5 |0 ≤ x ≤ 60{ }
c)
€
A = 10x + 5 |0 ≤ x ≤ 6{ }
d)
€
A = 5x |1≤ x ≤13{ }
25.
List
the
power
set
€
P S( )
for
the
set
€
S = A,B,C,D,F{ }
a)
€
P(S) ={∅, A{ }, B{ }, C{ }, D{ }, F{ }, A,B{ }, A,C{ }, A,D{ }, A,F{ }, B,C{ }, B,D{ }, B,F{ }, C,D{ }, C,F{ }, D,F{ },
€
A,B,C{ }, A,B,D{ }, A,B,F{ }, A,C,D{ }, A,C,F{ }, A,D,F{ }, B,C,D{ }, B,C,F{ }, B,D,F{ }, C,D,F{ },
€
A,B,C,D{ }, A,B,C,F{ }, A,C,D,F{ }, A,B,D,F{ } B,C,D,F{ }, A,B,C,D,F{ }}
b)
€
P(S) ={∅, A{ }, B{ }, C{ }, D{ }, F{ }, A,B{ }, A,C{ }, A,D{ }, A,F{ }, B,C{ }, B,D{ }, B,F{ }, C,D{ }, C,F{ }, D,F{ },
€
A,B,C{ }, A,B,D{ }, A,B,F{ }, A,C,D{ }, A,C,F{ }, A,D,F{ }, B,C,D{ }, B,C,F{ }, B,D,F{ }, C,D,F{ },
A,B,C,D,F{ }}
c)
€
P(S) = ∅, A{ }, B{ }, C{ }, D{ }, F{ }, A,B,C,D,F{ }{ }
d)
€
P(S) ={∅, A{ }, B{ }, C{ }, D{ }, F{ }, A,B{ }, A,C{ }, A,D{ }, A,F{ }, B,C{ }, B,D{ }, B,F{ }, C,D{ }, C,F{ }, D,F{ },
€
B,A{ }, C,A{ }, D,A{ }, F,A{ }, C,B{ }, D,B{ }, F,B{ }, D,C{ }, F,C{ }, F,D{ }, A,B,C{ }, C,B,A{ }, B,A,C{ },
C,D,F{ }, F,D,C{ }, A,B,C,D,F{ }}
