CISP 440 FINAL Question and answers
verified to pass 2025
There is a person in my class who is at least as old as every person in my
class.
What statements bellow equal the statement above ?
a. Some person in my class is at least as old as every person in my class.
b. Everyone is younger than a person in my class.
c. There is a person p in my class such that p is at least as old as every
person in my class.
d. There is a person in my class who is at least as old as every person.
e. There is a person p in my class with the property that for every person q in
my class, p is at least as old as q - correct answer a, c and e.
Is {0} = 0 ? - correct answer {0} ≠ 0 because {0} is a set with one element,
namely 0, whereas 0 is just the symbol that represents the number zero.
Let A = Z+, B = { n ∈ Z | 0 ≤ n ≤ 100}, and C = { 100, 200, 300, 400, 500 }.
Evaluate the truth and falsity of the following statement. - correct answer
False.
For example, 200 is in C but not in B.
Let A = { 2, 3, 4 } and B = { 6, 8, 10} and define a relation R from A to B as
follows: For all ( x, y ) ∈ A × B, ( x, y ) ∈ R means that yx is an integer.
a. Is 4 R 6 ?
b. Is 4 R 8 ?
c. Is ( 3, 8 ) ∈ R ?
d. Is ( 2, 10 ) ∈ R ? - correct answer a. No.
,b. Yes.
c. No.
d. Yes.
Let f be the squaring function f( x ) = x2.
What is f( −1 ), f( 0 ), and f( 12 )? - correct answer f ( −1 ) = ( −1 )^2 = 1,
f ( 0 ) = ( 0 )^2 = 0 ,
f ( 1/2 ) = ( 1/2 )^2 =1/4
What is an existential statement? - correct answer There is at least one thing
for which the property is true.
How many elements are in the set {1, {1}} ? - correct answer The set {1, {1}}
has two elements: 1 and the set whose only element is 1.
Use the set-roster notation to indicate the elements in the following set.
{ s ∈ Z | s >2 or s < 3 } - correct answer Z (every integer is in the set)
Define a relation S from R to R as follows:
For all ( x, y ) ∈ R × R, ( x, y ) ∈ S means that x ≥ y.
a. Is ( 2, 1 ) ∈ S ?
b. Is ( 2, 2 ) ∈ S ?
c. Is 2 S 3 ?
d. Is ( −1 ) S ( −2 ) ? - correct answer a. ( 2, 1 ) ∈ S because 2 ≥ 1.
b. ( 2, 2 ) ∈ S because 2 ≥ 2.
c. 2$3 because 2 < 3.
,d. (−1) S (−2) because −1 ≥ −2.
Let E = { 1, 2, 3 } and F = { −2, −1, 0 } and define a relation T from E to F as
follows: For all ( x, y ) ∈ E × F, ( x, y ) ∈ T means that x−y3 is an integer.
What is T as a set of ordered pairs? - correct answer T = { ( 1, −2 ), ( 2, −1 ),
( 3, 0 ) }
A universal statement asserts that a certain property is
___________________ for __________________________________. -
correct answer true; all elements of a set
Let A = Z+, B = { n ∈ Z | 0 ≤ n ≤ 100}, and C = { 100, 200, 300, 400, 500 }.
Evaluate the truth and falsity of the following statement.
B ⊆ A - correct answer False.
Zero is not a positive integer. Thus zero is in B but zero is not in A, and so B ⊈
A.
Is 4 = { 4 } ? - correct answer No,
{ 4 } is a set with one element, namely 4, whereas 4 is just a symbol that
represents the number 4.
Let A = { −1, 0, 1 } and B = { t, u, v, w }. Define a function F: A → B by the
following arrow diagram:
https://lrccd.instructure.com/assessment_questions/12021375/files/
10087939/download?
verifier=H5fQqXSNvPc0inR3RSW69Ix18u1c2vwRn6k4eAVe
, What is the domain and co-domain of F ? - correct answer Domain= A = { −1,
0, 1 }, co-domain = B= { t, u, v, w }
Given sets A and B, a relation from A to B is
__________________________________________________________. -
correct answer a subset of the Cartesian product A × B
There are real numbers u and v with the property that u + v < u − v.
What would be a less formal statement without variable and justification for
the truth or falsity of the statement? - correct answer There are real numbers
whose sum is less than their difference.
True.
sum:1+(−1)=0
difference: 1−(−1)=1+1=2
and 0 < 2.(sum is less than their difference)
Let A = {1,2,3}, B = {3,1,2}, and C = {1,1,2,3,3,3}. What are the elements of A,
B, and C? How are A, B, and C related? - correct answer A, B, and C have
exactly the same three elements: 1, 2, and 3. Therefore, A, B, and C are
simply different ways to represent the same set.
a. Is ( 5, −5 ) = ( −5, 5 ) ?
b. Is ( −2/−4 , (−2)^3 ) = ( 3/6 , −8 ) ? - correct answer a. No: For two ordered
pairs to be equal, the elements in each pair must occur in the same order. In
this case the first element of the first pair is 5, whereas the first element of the
second pair is —5, and the second element of the first pair is —5 whereas the
second element of the second pair is 5.
b. Yes: Both pairs have the same elements 1/2 and —8.
verified to pass 2025
There is a person in my class who is at least as old as every person in my
class.
What statements bellow equal the statement above ?
a. Some person in my class is at least as old as every person in my class.
b. Everyone is younger than a person in my class.
c. There is a person p in my class such that p is at least as old as every
person in my class.
d. There is a person in my class who is at least as old as every person.
e. There is a person p in my class with the property that for every person q in
my class, p is at least as old as q - correct answer a, c and e.
Is {0} = 0 ? - correct answer {0} ≠ 0 because {0} is a set with one element,
namely 0, whereas 0 is just the symbol that represents the number zero.
Let A = Z+, B = { n ∈ Z | 0 ≤ n ≤ 100}, and C = { 100, 200, 300, 400, 500 }.
Evaluate the truth and falsity of the following statement. - correct answer
False.
For example, 200 is in C but not in B.
Let A = { 2, 3, 4 } and B = { 6, 8, 10} and define a relation R from A to B as
follows: For all ( x, y ) ∈ A × B, ( x, y ) ∈ R means that yx is an integer.
a. Is 4 R 6 ?
b. Is 4 R 8 ?
c. Is ( 3, 8 ) ∈ R ?
d. Is ( 2, 10 ) ∈ R ? - correct answer a. No.
,b. Yes.
c. No.
d. Yes.
Let f be the squaring function f( x ) = x2.
What is f( −1 ), f( 0 ), and f( 12 )? - correct answer f ( −1 ) = ( −1 )^2 = 1,
f ( 0 ) = ( 0 )^2 = 0 ,
f ( 1/2 ) = ( 1/2 )^2 =1/4
What is an existential statement? - correct answer There is at least one thing
for which the property is true.
How many elements are in the set {1, {1}} ? - correct answer The set {1, {1}}
has two elements: 1 and the set whose only element is 1.
Use the set-roster notation to indicate the elements in the following set.
{ s ∈ Z | s >2 or s < 3 } - correct answer Z (every integer is in the set)
Define a relation S from R to R as follows:
For all ( x, y ) ∈ R × R, ( x, y ) ∈ S means that x ≥ y.
a. Is ( 2, 1 ) ∈ S ?
b. Is ( 2, 2 ) ∈ S ?
c. Is 2 S 3 ?
d. Is ( −1 ) S ( −2 ) ? - correct answer a. ( 2, 1 ) ∈ S because 2 ≥ 1.
b. ( 2, 2 ) ∈ S because 2 ≥ 2.
c. 2$3 because 2 < 3.
,d. (−1) S (−2) because −1 ≥ −2.
Let E = { 1, 2, 3 } and F = { −2, −1, 0 } and define a relation T from E to F as
follows: For all ( x, y ) ∈ E × F, ( x, y ) ∈ T means that x−y3 is an integer.
What is T as a set of ordered pairs? - correct answer T = { ( 1, −2 ), ( 2, −1 ),
( 3, 0 ) }
A universal statement asserts that a certain property is
___________________ for __________________________________. -
correct answer true; all elements of a set
Let A = Z+, B = { n ∈ Z | 0 ≤ n ≤ 100}, and C = { 100, 200, 300, 400, 500 }.
Evaluate the truth and falsity of the following statement.
B ⊆ A - correct answer False.
Zero is not a positive integer. Thus zero is in B but zero is not in A, and so B ⊈
A.
Is 4 = { 4 } ? - correct answer No,
{ 4 } is a set with one element, namely 4, whereas 4 is just a symbol that
represents the number 4.
Let A = { −1, 0, 1 } and B = { t, u, v, w }. Define a function F: A → B by the
following arrow diagram:
https://lrccd.instructure.com/assessment_questions/12021375/files/
10087939/download?
verifier=H5fQqXSNvPc0inR3RSW69Ix18u1c2vwRn6k4eAVe
, What is the domain and co-domain of F ? - correct answer Domain= A = { −1,
0, 1 }, co-domain = B= { t, u, v, w }
Given sets A and B, a relation from A to B is
__________________________________________________________. -
correct answer a subset of the Cartesian product A × B
There are real numbers u and v with the property that u + v < u − v.
What would be a less formal statement without variable and justification for
the truth or falsity of the statement? - correct answer There are real numbers
whose sum is less than their difference.
True.
sum:1+(−1)=0
difference: 1−(−1)=1+1=2
and 0 < 2.(sum is less than their difference)
Let A = {1,2,3}, B = {3,1,2}, and C = {1,1,2,3,3,3}. What are the elements of A,
B, and C? How are A, B, and C related? - correct answer A, B, and C have
exactly the same three elements: 1, 2, and 3. Therefore, A, B, and C are
simply different ways to represent the same set.
a. Is ( 5, −5 ) = ( −5, 5 ) ?
b. Is ( −2/−4 , (−2)^3 ) = ( 3/6 , −8 ) ? - correct answer a. No: For two ordered
pairs to be equal, the elements in each pair must occur in the same order. In
this case the first element of the first pair is 5, whereas the first element of the
second pair is —5, and the second element of the first pair is —5 whereas the
second element of the second pair is 5.
b. Yes: Both pairs have the same elements 1/2 and —8.
