Click and drag the named related conditionals to their corresponding statements of the conditional statement "If it snows today, I will ski
tomorrow."
wont
today,
snow
does
ifsnows
only
tomorrow
Id
If
tomorrow.
today.
snowed
have
not
itwill
then
tomorrow,
Score:
56.
269.90/340
Award: 10 out of 10.00 points
Points
79.38
%
Identify the correct statements for the given functions of set cfw_a, b, c, d to itself.
f(a) = b, f(b) = a, f(c) = c, f(d) = d is a one-to-one function as each element is an image of
ex
Score:
14.
269.90/340
Award: 1.12 out of 3.34 points
Points
79.38
%
Match the named related conditionals (in the left column) to their corresponding statements (in
the right column) of the conditional statement"I come to class whenever there is going to
Score:
36.
Award: 1.66 out of 1.66 points
269.90/340
Points
79.38
%
Is all the truth values of the following truth table of the conditional statement (p q) p represents tautology is correct.
p
q
pq
(p q)
(p q) p
T
T
F
F
T
F
T
F
T
F
T
T
F
T
F
F
Yes
No
Ref
Lei; Phi) he the proposition that
3 divides 3 + 2n.
H tlivitiHH i3+2-1 .~ which is l.r|:*1 ai|i:e13+2-1 : 3,
and 3 divides 3.
liIULLUHVB GILL-3p: bul Lllh
3 divides k3 + 21.- for an arbitrary integer is a D.
awnnu .1 '-I-I-'|-"-
W: :3
Score:
269.90/340
Points
79.38
%
An explorer is captured by a group of cannibals. There are two types of cannibalsthose who
always tell the truth and those who always lie. The cannibals will barbecue the explorer unless
he can determine whether a particu
Score:
29.
269.90/340
Award: 2.50 out of 2.50 points
Points
79.38
%
Find the negation of the statement "Yoshiko knows Java and calculus" using De Morgan's law.
Yoshiko knows Java and does not know calculus.
Yoshiko does not know Java and does not know ca
Score:
37.
Award: 1.66 out of 1.66 points
269.90/340
Points
79.38
%
Identify the missing truth values from the following truth table of the conditional statement (p q) q.
p
q
pq
(p q)
q
T
T
F
F
T
F
T
F
F
T
F
F
F
T
F
T
pq
T
F
T
T
pq
F
F
T
T
pq
T
F
F
T
pq
Click and drag statements to ll in the details of showing that was; . PH: + 1) is true, thereby eempieting the induction step.
(k+l3+2cfw_k+l=cfw_k3+3k2+3k+l+[2k+2)
=(h3+5k) Hit? +1)
[kt 1] i 2: i ij=(it=1 i at:2 i 3&- | 1) i (2:.- | 2]
=(Ic3+2k+3l[k9+k+l
Score:
34.
Award: 0 out of 1.66 points
269.90/340
Points
79.38
%
The following truth table of the conditional statement p (p q) is tautology.
p
q
p
pq
T
T
F
F
T
F
T
F
F
F
T
T
T
F
T
A
In the above truth table the truth value of variable A is _.
F
Correct:
Score:
269.90/340
Points
79.38
%
Consider the statement, Whenever the system software is being upgraded, users cannot access
the file system. If users can access the file system, then they can save new files. If users cannot
save new files,then the syste
Score:
17.
269.90/340
Award: 0 out of 1.67 points
Points
79.38
%
The truth table of the compound proposition p (qr) is as follows:
p
q
r
p
(q r)
T
T
T
T
F
F
F
F
T
T
F
F
T
T
F
F
T
F
T
F
T
F
T
F
T
T
T
T
T
T
T
The output of the sixth row in the truth table
Score:
30.
269.90/340
Award: 2.50 out of 2.50 points
Points
79.38
%
The negation of the statement "James is young and strong" using De Morgan's law is "James is
not young, or he is not strong."
Is it true?
Yes
No
The negation of the statement "James is y
23.
hward: 10 out of 10.131?! points
What is the largest n for which one can solve within one second a problem
functions tin below? Click and drag the correct answer to complete each s'
For f(n) = log n, the largest n is
For f0) = n, the largest in is I t
Score:
21.
269.90/340
Points
79.38
%
Award: 1.67 out of 1.67 points
The truth table of the compound proposition (p q) (q r) is as follows:
p
q
r
p
q
p q
qr
(p q) (q r)
T
T
T
F
F
T
T
T
T
T
T
F
F
F
F
T
F
F
T
T
F
F
F
T
F
T
F
T
F
F
F
F
T
T
T
T
F
T
T
F
F
T
T
Score:
269.90/340
Points
79.38
%
16.
Award: 1.67 out of 1.67 points
Identify the output column of the given truth table of the compound proposition p (q
p
q
r
q
q r
T
T
T
F
T
T
T
F
F
F
T
F
T
T
T
T
F
F
T
T
F
F
F
F
T
T
F
F
T
F
T
F
F
F
T
T
T
F
T
T
p (q
r)
T
Score:
43.
250.18/280
89.35
Points
Award: 10 out of 10.00 points
Arrange the given steps in the correct order to prove that
6, using mathematical induction.
4
<
Correct: 4
3
=3
Correct: 3
1
For n = 7,
= 2187 < 7! = 5040.
Correct: 1
2
Suppose that for som
Score:
269.90/340
Points
79.38
%
Find the sum-of-products expansions of the the following Boolean functions.
85.
Award: 2.50 out of 2.50 points
a)
The function has the value 1 whenever at least one of the variables has the value 1. There are
seven minter
Score:
24.
250.18/280
Award: 10 out of 10.00 points
Points
89.35
%
Match the size n (in the left column) to the time that an algorithm takes to solve a problem of
size n (in the right column), if this algorithm uses 2n2 + 2n operations, each requiring 10
Score:
269.90/340
Points
79.38
%
Find the values, if any, of the Boolean variable x that satisfy these equations.
73.
Award: 2.50 out of 2.50 points
a)
x=0
x = 0 and x = 1
There are no solutions.
x=1
74.
Award: 2.50 out of 2.50 points
b)
There are no
Score:
51.
269.90/340
Award: 2 out of 2.00 points
Points
79.38
%
The floor value of 1.1 is _.
1
The floor function assigns to the real number xthe largest integer that is less than or equal to x.
Score:
250.18/280
Points
89.35
%
Find f(2), f(3), f(4), and f(5) if f is defined recursively by f(0) = 1, f(1) = 2, and f(n + 1) = f(n) + 3f(n 1)
for n = 1,2,.
References
Section Break
47.
Chapter: 05
Induction and
Recursion
Award: 0.83 out of 0.83 point
Score:
269.90/340
Points
79.38
%
Select either the varaible or its complement for each of the three variables in the product of the
Boolean variables x, y, and z or their complements that gives the Boolean product of value 1 if
and only if
81.
Award: 2.5
CIlick and diglg the steps given in the light, to the corresponding step names given in the Ie, to prove that irAL A2, An and 31- 32. 3n are sets such that AJC 8.? fat: 1, 2, 3 , n, then
2': JUAJE J=1UBJ'.
Inductive hypothesis
Hillier .'L UILI A-IJ- 01' .
Score:
33.
Award: 1.66 out of 1.66 points
269.90/340
Points
79.38
%
Identify the missing truth values from the following truth table of the conditional statement p (p q).
p
q
pq
T
T
F
F
T
F
T
F
pq
T
F
T
F
pq
T
F
F
F
pq
T
T
T
F
pq
F
T
T
F
References
Multi
Score:
15.
269.90/340
Award: 3.34 out of 3.34 points
Points
79.38
%
Match the named related conditionals (in the left column) to their corresponding statements (in
the right column) of the conditional statement"A positive integer is a prime only if it ha
Score:
35.
269.90/340
Award: 1.67 out of 1.67 points
Points
79.38
%
In the following truth table the truth value of the conditional statement (p q) (p q) of
missing term is _.
p
q
pq
p q (p q)
(p q)
T
T
F
F
T
F
T
F
T
F
F
T
F
T
T
T
T
T
T
F
References
Fil
Probability problems (continued)
1. On a safe there are four alarms which are arranged so that any one will sound when someone tries
to break into the safe. If the probability that each alarm will function properly is 0.85, find the
probability that at le
COMP2100 Probability Problems
1. Susan takes examinations in mathematics, French and history. The probability that she passes
each is 0.7, 0.8 and 0.6, respectively. Given that her performances in each subject are
independent, draw a tree diagram to show