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Discrete Mathematics and its Applications

Kenneth H. Rosen

$Math Studyset Vaia Explanations$ Math

7th Edition · 808 pages

ISBN: 9780073383095

Chapter 2: Q35E (page 126)

How many different elements does A X B have if A has m elements and B has n elements

Short Answer

Expert verified

m X n

Step by step solution

Number of elements in a set

If X is an element of Y

Notation:$X \in Y$

The number of elements in it will be $x \times y$.

To find different number of elements

Number of elements in set $A = m$

Number of elements in set $B = n$

Therefore, number of elements in $A \times B = m \times n$

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Most popular questions from this chapter

Question: Find $f \circ g$ and $g \circ f$ , where $f (x) = x^{2} + 1$ and $g (x) = x + 2$ , are functions from $ℝ t o ℝ$ .

Construct a truth table for each of these compound propositions.

a. $(p \lor q) \to (p \oplus q)$

b.. $(p \oplus q) \to (p \land q)$

c. $(p \lor q) \oplus (p \land q)$

d. $(p \leftrightarrow q) \oplus (\neg p \leftrightarrow q)$

e. $(p \leftrightarrow q) \oplus (\neg p \leftrightarrow \neg r)$

f. $(p \oplus q) \to (p \oplus \neg q)$

If f and $f \circ g$ are one-to-one, does it follow that g is one-to-one? Justify your answer.

For each of these partial functions, determine its domain, codomain, domain of definition, and the set of values for which it is undefined. Also, determine whether it is a total function.

$\begin{aligned} (a) f : Z \to R, f (n) = 1 / n \\ (b) f : Z \to Z, f (n) = ⌈ n / 2 ⌉ \\ (c) f : Z \times Z \to Q, f (m, n) = m / n \\ (d) f : Z \times Z \to Z, f (m, n) = mn \\ (e) f : Z \times Z \to Z, f (m, n) = m - nifm > n \end{aligned}$

Determine whether each of these functions is a bijection from R to R.

$f (x) = - 3 x + 4$
$f (x) = - 3 x^{2} + 7$
role="math" localid="1668414131444" $f (x) = (x + 1) / (x + 2)$
role="math" localid="1668414147841" $f (x) = x^{5} + 1$

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How many different elements does A X B have if A has m elements and B has n elements

Short Answer

Step by step solution

Number of elements in a set

To find different number of elements

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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