Section 5.4
2.
3.
10.
26.
Section 6.1
1.
12.
14.
a.
17.
b.
A.
D.
20.
23.
B.
C.
E.
F.
Section 6.2
9. Use an element argument to prove the statement in 9. Assume that all sets are subsets of a
universal set U.
23.
31. Use the element method for proving a se

Section 7.4
5.
15.
20.
1
Section 8.1
5.
8.
2
14.
Section 8.2
14. Determine whether the given relation in 14, 22, and 26 is reflexive, symmetric, transitive, or none of
these. Justify your answers.
22.
3
26.
4

Section 9.1
8. Write each of the following events as a set and compute its probability
The event that the numbers showing face up are the same
10. The event that the sum of the numbers showing face up is at least 9.
13.
20.
1
Section 9.2
15.
23.
2
26. Det

Chapter 2, Section 2.1
8. Write the statements in symbolic form using the symbols , and and the indicated letters
to represent component statements.
Let h = John is healthy, w = John is wealthy, and s = John is wise.
a. John is healthy and wealthy but not

Consider the universal conditional statement
x D, P(x) Q(x)
(i) The contrapositive of this statement is
x D, Q(x) P(x)
(ii) The converse of this statement is
x D, Q(x) P(x)
(iii) The inverse of this statement is
x D, P(x) Q(x)
Existential Conditional Stat

Section 3.2
2. Which of the following is a negation for All dogs are loyal? More than one answer may be
correct.
C. Some dogs are disloyal.
F. There is a dog that is disloyal.
10. Write a negation for statement in 10.
computer programs P, if P compiles w

1
2. Write the first four terms of the sequences defined by the formulas
bj = (5 j)/(5 + j) , for all integers j 1.
b1 = 4/6 = 2/3 ; b2 = 3/7 ; b3 = 2/8 = 1/4 ; b4= 1/9
7. Let ak = 2k + 1 and bk = (k 1)3 + k + 2 for all integers k 0. Show that the first t

Section 5.2
2. Use mathematical induction to show that any postage of at least 12 can be obtained using 3
and 7 stamps.
Proof: Let P(n) be the property n cents can be obtained by using 3-cent and 7-cent coins.
Show that P(12) is true:
12 cents can be obta

Section 2.2
22. Write contrapositives for the statements of exercise 20.
B. If today is New Years Eve, then tomorrow is January
If tomorrow is not January , then today is not New Year's Eve.
E. If x is nonnegative, then x is positive or x is 0.
If x is no

4. For each integer n with n 2, let P(n) be the formula
a. Write P(2). Is P(2) true?
b. Write P(k).
c. Write P(k + 1).
d. In a proof by mathematical induction that the formula holds for all integers n 2, what must
be shown in the inductive step?
14. Prove