Bridge to Abstract Mathematics: Mathematical Proof and Structures

1.5 COUNTING PROPERTIES OF FINITE SETS (OPTIONAL) 43 We emphasize that the content of this article is restricted to finite sets. ...

44 SETS Chapter 1 that n(A u B) = 36, n(A) = 24, and n(B) = 28. By Counting Formula 1, n(A n B) = n(A) + n(B) - n(A u B) = 24 + ...

1.5 COUNTING PROPERTIES OF FINITE SETS (OPTIONAL) 45 In the problem posed just before the statement of Counting Formula 2, we ha ...

46 SETS Chapter 1 The rationale behind Formula 3, as illustrated in Example 2, is that there are k activities to be performed an ...

1.5 COUNTING PROPERTIES OF FINITE SETS (OPTIONAL) 47 a1 a2 a3 am-1 am Figure 1 .I 1 A device for representing pictorially the p ...

48 SETS Chapter 1 k (0 5 k 5 m), this becomes C(m, k) = P(m, k)/P(k, k) = m!/(m - k)!k!. This is the formula for the number of k ...

1.5 COUNTING PROPERTIES OF FINITE SETS (OPTIONAL) 49 ization in mathematics. Example 5 showed that, even when the universal set ...

50 SETS Chapter 1 (a) How many 5-card poker hands can be dealt from a deck of 52 cards? *(b) If five cards are dealt consecutiv ...

1.5 COUNTING PROPERTIES OF FINITE SETS (OPTIONAL) 51 Figure 1.12 * a b C (c) Let U = (1,2,3,... ,9, 10). Use the formula from pa ...

LOGIC, PART I: THE PROPOSITIONAL CALCULUS CHAPTER 2 Consider the sentence "Mathematics is a complicated subject, and in order to ...

2.1 BASIC CONCEPTS OF THE PROPOSITIONAL CALCULUS 53 at this point, write a positive statement corresponding to L # lim,,, f(x)? ...

54 LOGIC, PART I: THE PROPOSITIONAL CALCULUS Chapter 2 The designation T(true) or F(false), one and only one of which is assigna ...

2.1 BASIC CONCEPTS OF THE PROPOSITIONAL CALCULUS 55 we mean "for every x, x(x + 4) = x2 + 4x," and treat the former as a (true) ...

56 LOGIC. PART I: THE PROPOSITIONAL CALCULUS Chapter 2 know the truth values of p and q, and not p and q themselves. Clearly the ...

2.1 BASIC CONCEPTS OF THE PROPOSITIONAL CALCULUS 57 Figure 2.1 Truth tables for negation, conjunction, and disjunction. EXAMPLE ...

58 LOGIC, PART I: THE PROPOSITIONAL CALCULUS Chapter 2 FTT T T F T FFT T F F F Figure 2.2 The statement form (-p A q) v (p A r) ...

2.2 TAUTOLOGY, EQUIVALENCE, THE CONDITIONAL, AND BICONDITIONAL 59 Determine whether each of the following statements is true or ...

60 LOGIC, PART I: THE PROPOSITIONAL CALCULUS Chapter 2 Figure 2.3 The statement form p A -p is always false, whereas p v - p is ...

2.2 TAUTOLOGY, EQUIVALENCE, THE CONDITIONAL, AND BICONDITIONAL 61 A consequence of Example 2 is that, if one person claims and i ...

62 LOGIC, PART I: THE PROPOSITIONAL CALCULUS Chapter 2 Examples of conditionals include: If I finish my work, I go out on the t ...