MATH. 122 A01 & A02 December 2014 1
1. [3] Find all truth values for p, q and r for which (p > q) 4) r is true.
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2. [4] Use known logic
MATH 122 A01, A02, A03, & A04 April 2016 ' 1
1. [4] Suppose the statement p <) q is false. Find all combinations of truth values for p, q,
and 7" such that the statement (or H p) V (r /\ g) is true. ._
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201701 Math 122 [A05] Quiz #2
Name: SOLUT 0N5 VOO# Score: / 15
This quiz consists of 6 questions on 3 pages. The time limit is 25 minutes. Math and Stats
standard calculators are allowed, but calculators will not help with these questions! To
achieve full
201'701 Math 122 [A02] Quiz #1
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achiev
201701 Math 122' [A05] Quiz #6
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201701 Math 122 [A05] Quiz #4
Name: SOLUT IONS , VOO# Score: / 15
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201701 Math 122 [A02] Quiz #4
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This quiz consists of 7 questions on 2 pages. The timeslimit is 25 minutes. Math and Stats
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201701 Math 122 [A02] Quiz #5
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201701; Math 122 [A02]. Quiz #3
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201701 Math 122 [A05] Quiz #1
Name: SOLUTl CNS VOO# Score: / 15
'This quiz consists of 6 questions on 2 pages. The time limit is 25 minutes. Math'and Stats
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achieve
- 201701 Math 122 [A05] Quiz #3
Name: SOLu'rIONS VOO# Score: / 15
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201701 Math 122 [A02] Quiz #6
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201701. Math 122 [A05] Quiz #5
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Math 122
In-class Assignment 7
Wednesday, February 22nd 2017
Name:
V00#:
You are strongly encouraged to talk to each other, and to the instructor. You must show
all of your work to receive full marks. Set up your page as follows, you do not need to
rewrit
Further Questions on Sets and Cartesian Products
1. Let A, B, C be subsets of some universal set U. Use the laws of De
Morgan and any other set theoretic identities we have discussed to
prove the following:
(a) (A\B)\C = A\(B C)
(b) A\(B\C) = (A\B) (A\C C
Math 122
In-class Assignment 12
Solutions
Let A = cfw_1, 2, 3, 4. Write an expression for each of the following.
You do not need to simplify.
(a) What is A A?
A A = A A = (4)(4) = 16
(b) How many relations on A are there?
2AA = 216 = 65536
(c) What is P(A
Math 122
In-class Assignment 2
Solutions
Use common logical equivalences to prove the logical equivalence.
You will not receive credit for using a truth table.
(p q) q) (p q)
(p q) q)
(p q) q
(p) q) q
(p q) q
(p q) (q q)
(p q) (1)
(p q).
By known logical
Math 122
In-class Assignment 11
Name:
V00#:
You are strongly encouraged to talk to each other, and to the instructor.
You must show all of your work to receive full marks. Set up your page as
follows, you do not need to rewrite the question.
Use the blank
Math 122
Inclass Assignment 10
Name: SOL uT. QNS p V0#:
You are strongly encouraged to talk to each other, and to the instructor.
You must show all of your work to receive full marks; Set up your page as
follows, you do not need to rewrite the question.
F
Math 122
In-class Assignment 8
Monday, March 6th 2017
V00#:
Name:
You are strongly encouraged to talk to each other, and to the instructor.
You must show all of your work to receive full marks. Set up your page as
follows, you do not need to rewrite the q
Math 122
In-class Assignment 1
Thursday, January 5th, 2016
Solutions
Given the following statements:
p: 242 is even.
q: 92 > 0.
Use the blank to indicate whether each of the following statements
is TRUE (T) or FALSE (F). No justification is necessary. You
Math & Stats Assistance Centre
David Turpin Building
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MATH 101 Review
Part I: Graphical Applications of Integration
1. Consider the region in the first quadrant bounded by the curves y = x3 and y = x. Find th
Math 101
Warming up
Due at the beginning of tutorial on January 16
1. Explain why the following calculation is incorrect.
1
Z 1
1
1
1
1
dx = =
= 2.
2
x 1
1
1
1 x
Note: We are not asking you to evaluate this integral, because we dont yet have the too
Math 101
Parts and trigonometry
Due at the beginning of tutorial on January 23
1. While we often use trigonometric substitutions for integrals where expressions like
sometimes Z
there are other approaches. This question is one such example.
p
x
Show that
Math 101
Volumes
Due at the beginning of tutorial on February 6
1. Let R be the region in the plane bounded by y ex = 1, x = 0, x = 1, and y = 0.
(a) Sketch R.
(b) Find the volume of the solid obtained by rotating R around the x-axis.
(c) Find the volume
Math 101
Warming up
Due at the beginning of tutorial on January 16
1. Explain why the following calculation is incorrect.
1
Z 1
1
1
1
1
dx = =
= 2.
2
x 1
1
1
1 x
Note: We are not asking you to evaluate this integral, because we dont yet have the too
Math 101
Volumes
Due at the beginning of tutorial on February 6
1. Let R be the region in the plane bounded by y ex = 1, x = 0, x = 1, and y = 0.
(a) Sketch R.
(b) Find the volume of the solid obtained by rotating R around the x-axis.
(c) Find the volume
Math 101
Parts and trigonometry
Due at the beginning of tutorial on January 23
1. While we often use trigonometric substitutions for integrals where expressions like
sometimes Z
there are other approaches. This question is one such example.
p
x
Show that
Math 101
Partially improper
Not to be handed in
1. Use partial fractions to find the following antiderivatives.
Z 2
x 4x + 1
(a)
dx
x2 2x + 1
Z
1
dx
(b)
x3 + 4x
Z
sin(x)
(c)
csc(x) dx Hint: Start by showing that csc(x) =
, then do a substitution to turn t
Euclidean Algorithm. Let a and b be natural numbers with b < a. To
find the greatest common divisor of a and b, write
a = q1 b + r1 , with 0 r1 < b,
If r1 0, then write b = q2 r1 + r2 , with 0 r2 < r1 ,
If r2 0, then write r1 = q3 r2 + r3 , with 0 r3 < r2