(a) List all subsets of A = {a}. 0 () ○ {a} (a) ○ {}, {a} How many subsets does A have? subsets (b) List all subsets of A= (a, b). Ⓒ (b) ○ {}, (a), (b) (a), (b) ○ {} O {}, (a), (b), (a, b) How many subsets does A have? subsets (c) List all subsets of A= (a, b, c). ○ {}, {a}, {b}, {a, b}, {a, c), (a, b, c) (), (a), (b), (c), (a, b), (a, c) (a), (c), (a, b), (a, c), (a, b, c) (a), (b), (c) ○ {}, (a), (b), (c), (a, b), (a, c), (b, c), (a, b, c) How many subsets does A have? subsets (d) List all subsets of A= (a, b, c, d). ○ {}, (a), (b), (c), (d), (a, b}, {a, c), (a, d), (b, c), (b, d), (c,d), (a, b, c), (a, b, d), (a, c, d), (b, c, d), (a, b, c, d} ○ {}, (a), (b), (c), (d), (a, b), {a, c), {a, d), (b, c), (b, d), (a, b, c), (a, b, d), (b, c, d) ○ {}, (a), (b), (c), (d), (a, b), (a, c), (b, c), (b, d), (c, d), (a, b, c), (a, b, d}, {a, c, d), (b, c, d) ○ {}, (b), (c), (d), (a, b}, {a, c), {a, d), (b, c), {c, d), (a, b, c), (a, c, d), (b, c, d), (a, b, c, d) ○ {}, (a), (d), (a, b), (a, c), {a, d), (b, c), (b, d), (a, b, c), (a, b, d), {a, c, d), (b, c, d), (a, b, c, d) How many subsets does A have? subsets (e) Is there a relationship between the cardinal number of set A and the number of subsets of set A? Yes, the number of subsets of A= 2n(A), Yes, the number of subsets of A = n(A)². Yes, the number of subsets of A = 2n(A). O O O No (f) How many subsets does A = (a, b, c, d, e, f) have? subsets

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Question Details**

**(a)** List all subsets of \( A = \{a\} \).

- \( \{\} \)
- \( \{a\} \)
- \( \{\}, \{a\} \)

How many subsets does \( A \) have?  
\[ \_\_\_\_ \text{ subsets} \]

**(b)** List all subsets of \( A = \{a, b\} \).

- \( \{b\} \)
- \( \{\}, \{a\}, \{b\} \)
- \( \{a\}, \{b\} \)
- \( \{\} \)
- \( \{\}, \{a\}, \{b\}, \{a, b\} \)

How many subsets does \( A \) have?  
\[ \_\_\_\_ \text{ subsets} \]

**(c)** List all subsets of \( A = \{a, b, c\} \).

- \( \{\}, \{a\}, \{b\}, \{c\}, \{a, b\}, \{a, c\}, \{b, c\}, \{a, b, c\} \)
- \( \{\}, \{a\}, \{b\}, \{c\}, \{a, b\}, \{a, c\} \)
- \( \{a\}, \{b\}, \{c\} \)
- \( \{\}, \{a\}, \{b\}, \{c\}, \{a, b\}, \{a, c\}, \{b, c\}, \{a, b, c\} \)

How many subsets does \( A \) have?  
\[ \_\_\_\_ \text{ subsets} \]

**(d)** List all subsets of \( A = \{a, b, c, d\} \).

- \( \{\}, \{a\}, \{b\}, \{c\}, \{d\}, \{a, b\}, \{a, c\}, \{a, d\}, \{b, c\}, \{b, d\}, \{c, d\}, \{a, b, c\}, \{a, b,
Transcribed Image Text:**Question Details** **(a)** List all subsets of \( A = \{a\} \). - \( \{\} \) - \( \{a\} \) - \( \{\}, \{a\} \) How many subsets does \( A \) have? \[ \_\_\_\_ \text{ subsets} \] **(b)** List all subsets of \( A = \{a, b\} \). - \( \{b\} \) - \( \{\}, \{a\}, \{b\} \) - \( \{a\}, \{b\} \) - \( \{\} \) - \( \{\}, \{a\}, \{b\}, \{a, b\} \) How many subsets does \( A \) have? \[ \_\_\_\_ \text{ subsets} \] **(c)** List all subsets of \( A = \{a, b, c\} \). - \( \{\}, \{a\}, \{b\}, \{c\}, \{a, b\}, \{a, c\}, \{b, c\}, \{a, b, c\} \) - \( \{\}, \{a\}, \{b\}, \{c\}, \{a, b\}, \{a, c\} \) - \( \{a\}, \{b\}, \{c\} \) - \( \{\}, \{a\}, \{b\}, \{c\}, \{a, b\}, \{a, c\}, \{b, c\}, \{a, b, c\} \) How many subsets does \( A \) have? \[ \_\_\_\_ \text{ subsets} \] **(d)** List all subsets of \( A = \{a, b, c, d\} \). - \( \{\}, \{a\}, \{b\}, \{c\}, \{d\}, \{a, b\}, \{a, c\}, \{a, d\}, \{b, c\}, \{b, d\}, \{c, d\}, \{a, b, c\}, \{a, b,
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