Homework for Section 2.7
Dominique Dec
May 24, 2015
Section 2.7
7.3 Find the range of each function f : R R.
1. f (x) = x2 + 2, Rng f = [2, )
2. f (x) = (x + 4)2 3. Rng f = [3, )
3. f (x) = x2 + 6x 4. Rng f = [13, )
4. f (x) = 3 cos(5). Rng f = [3, 3]
7.5
Homework for Sections 2.5 and 2.6
Dominique Dec
May 24, 2015
Section 2.5
5.10 Fill in the blanks in the proof of the following theorem.
Theorem: A B, A B = B.
Proof. Suppose that A B. If x A B, then x A or [x B]. Since A B, in either case we have
x B. Thu
Corrected work from Section 2.5, 2.6, and 2.7
Dominique Dec
June 3, 2015
Section 2.5
5.17 Which statement(s) below would enable one ot conclude that x A \ B. If (A \ B) = cfw_x : x
/
A and x B = (A \ B) = cfw_x : x A or x B.
/
/
1. x A B
/
2. x B
3. x A
Homework for Section 3.10
Dominique Dec
June 3, 2015
Section 3.10
10.3 Prove that 11 + 22 + . . . + n2 =
n(n + 1)(n + 2)
for all n N.
6
23
Proof. For n = 1 the statement is obviously true since 12 = 1 and
= 1 as well. We now assume
6
that the statment wil
Homework for Sections 1.3 and 1.4
Dominique Dec
May 15, 2015
Section 1.3
3.1 Mark each statment True or False. Justify each answer.
1. What an implication p = q is used as a theorem, we refer to p as the antecedent. TRUE
2. The contrapositive of p = q is
Homework 1.1 and 1.2
Dominique Dec
May 16, 2015
Section 1.1
1.4 Write the negation of each statement:
1. The relation R is transitive. The relation R is not transitive.
2. The set of rational numbers is bounded. The set of rational numbers is unbounded.
3