MATH 2020 - SOLUTIONS TO HW 8, DUE APRIL 2
2.2.4: Let A = cfw_a, b, c, d, e and B = cfw_a, b, c, d, e, f, g, h. Find the following sets:
(a)
(b)
(c)
(d)
A B = cfw_a, b, c, d, e, f, g, h
A B = cfw_a, b, c, d, e
AB =
B A = cfw_f, g, h
2.2.6: Prove the Ident
Partial Solution to part of 2.3 70(e) For real numbers x, y , Either prove or disprove that x + y + x + y 2x + 2y Recall that we can write x = x + cfw_ x where cfw_x is the fractional part of x, which is a number in [0, 1). There are 4 cases: 1) cfw_x [0,
MATH 2020 - SOLUTIONS TO HW 9, DUE APRIL 11
4.1.2: Prove that if a is a non-zero integer, then:
(a) 1 divides a.
Proof. Let a Z cfw_0. Then a = 1 a, and therefore 1|a.
(b) a divides 0.
Proof. Again, let a Z cfw_0. Then, 0 = a 0, and therefore a|0.
4.1.8:
MATH 2020 - SOLUTIONS TO HW 6, DUE MARCH 21
1.8.14: Prove or disprove that if a and b are rational numbers, then ab is also rational.
Proof. This statement is false. Let a = 2 and b = 1 . Then, a and b are both rational,
2
1
and ab = 2 2 = 2 which we have
MATH 2020 - SOLUTIONS TO HW 5, DUE MARCH 14
1.7.16: Prove that if m and n are integers and mn is even, then either m is even or
n is even.
Proof. Let m and n be integers such that mn is even. We show that m is even or
n is even. For the sake of contradict
MATH 2020 - SOLUTIONS TO HW 7, DUE MARCH 28
2.1.6: Suppose that A = cfw_2, 4, 6, B = cfw_2, 6, C = cfw_4, 6, and D = cfw_4, 6, 8. Determine which of these sets are subsets of which other of these sets.
BA
CA
CD
2.1.18: Find two sets A and B such that A
HOMEWORK Due Wednesday October 14: From section 2.1 of text book: 2, 8, 18, 20, 32 From section 2.2 of text book: 2, 4, 6, 8, 14
Preparation for Quiz Wednesday October 7: Let A and B and C be subsets of the set of all integers Z, dened by A= B C (1) (2) (
Math2020 Homework Due Last Week of Semester:
Due Wed Dec 2: 4.2 ex 4, 6, 10, 14, 20, 32 Due Fri Dec 4: 5.3 ex 2, 4, 8, 22, 24
Math2020 Quiz on Monday November 30
Compute the value of
5 3
. (Or compute
n r
for any small values of n and r.)
Math2020 Final E
Math2020 Solutions to question 7 of nal guide
(1) (a) How many ways are there to select three dierent pieces of fruit from a bowl of 5 dierent fruits? SOLUTION: Ways to choose 3 from 5 is 5 3 = 543 = 10 123
(b) You go to the supermarket to buy three peice
Quiz 2: Let p and q be the following propositions: p : the pie is opened q : the birds begin to sing Part I Match up the English sentences (1)-(5) with the corresponding logical proposition (a)-(e). Write your answers in the boxes. (1) When the pie is ope
HOMEWORK 2
Homework 1: Due Wednesday September 9: From section 1.2 of text book: 2, 4, 6, 10, 40 From section 1.3 of text book: 2, 8, 10, 12, 32 Preparation for Quiz 2: (We'll go through the solutions on Wednesday) The quiz on Friday September 4 will be s
Test 2 Guide: Test 2 will have questions on the following topics. See the given sections of the text book for more details. (1) 1.6 Direct proof. You will be asked to prove one of the following (or very similar) using a direct proof: If m and n are both s