Activity 15-Power Sets and Partitions start time: Model I. (25min) Partitions. N

Question

Activity 15-Power Sets and Partitions start time: Model I. (25min) Partitions. NAME Let A- (1, 2, 3, 4, 5, 6) We can form new sets using the elements of set A. The following are sets of sets which havea ? K1, 2). {4, 3}.(5). (6)) This set has 4 elements, each of which is a set. C {{1, 5, 3, 4, 2, 6)) This set has only one element which is itself a set Explore the model 1. What are the elements of set A? 2. How many elements in set B 3. What are the elements of B? [Be careful, set B is a set of sets] 4. How many elements in set C? What are the elements) of set C? Sets B and C are a special type of set. Notice all the elements in Set A are contained in a 'member set' of B and C. Also notice that no element is in more than one member set. Sets B and C are called partitions of Set A A partition of a set A is a set S of non-empty subsets of A satisfying the following O If P1 and P2 are two different members of S, then P1nP2 0. (That is, distinct parts are disjoint.) O The union of all of the members of S is the entire set A. Critical Thinking 5. Create another partition for Set A with 2 parts. With 3 parts. page 1

Explanation / Answer

Solution:

The first four subparts have been answered as per Chegg guidelines, please repost others.

1)

The element of set A are:

1, 2, 3, 4, 5, 6.

2)

4 elements are there and they are set themselves.

3)

The elements of B are:

{1, 2}, {4, 3}, {5}, {6}

4)

6 elements are in set C

5)

partition with two parts.

{{1, 2, 3}, {4, 5, 6}}

partition with three parts.

{{1, 2}, {3, 4}, {5, 6}}

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