   # a. Is {{a, d , e}, { b , c}, { d , f }} a partition of { a , b, c, d, e, f}? b. Is {{ w, x, v), { u, y , q }, {p. z }} a partition of { p q , u, v ,w, x,y,z }? c. Is {{5, 4), {7, 2}, {1, 3, 4}, {6, 8}} a partition of {1, 2, 3, 4, 5, 6, 7, 8}? d. Is {{3, 7, 8}, {2, 9}, {1,4,5}} a partition of {1, 2, 3, 4, 5, 6, 7, 8, 9}? e. Is {{1, 5}, {4, 7}, {2, 8, 6, 3}} a partition of {1, 2, 3, 4, 5, 6, 7, 8}? ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
Publisher: Cengage Learning,
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
Publisher: Cengage Learning,
ISBN: 9781337694193
Chapter 6.1, Problem 27ES
Textbook Problem
1 views

## a. Is {{a, d, e}, {b, c}, {d, f }} a partition of {a, b, c, d, e, f}? b. Is {{w, x, v), {u, y, q}, {p. z}} a partition of {p q, u, v ,w, x,y,z}? c. Is {{5, 4), {7, 2}, {1, 3, 4}, {6, 8}} a partition of {1, 2, 3, 4, 5, 6, 7, 8}? d. Is {{3, 7, 8}, {2, 9}, {1,4,5}} a partition of {1, 2, 3, 4, 5, 6, 7, 8, 9}? e. Is {{1, 5}, {4, 7}, {2, 8, 6, 3}} a partition of {1, 2, 3, 4, 5, 6, 7, 8}?

To determine

(a)

Find out whether {{a,d,e},{b,c},{d,f}} is a partition of {a,b,c,d,e,f} or not.

### Explanation of Solution

Calculation:

In a partition of a set each subset should occur distinct element.

The partition is as shown below.

{{a,d,e},{b,c},{d,f}}

The element d is in two of the sets

To determine

(b)

Find out whether {{w,x,v},{u,y,q},{p,z}} is a partition of {p,q,u,v,w,x,y,z} or not.

To determine

(c)

Find out whether {{5,4},{7,2},{1,3,4},{6,8}} is a partition of {1,2,3,4,5,6,7,8} or not.

To determine

(d)

Find out whether {{3,7,8},{2,9},{1,4,5}} is a partition of {1,2,3,4,5,6,7,8,9} or not.

To determine

(e)

Find out whether {{1,5},{4,7},{2,8,6,3}} is a partition of {1,2,3,4,5,6,7,8} or not.

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