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Which of these collections of subsets are partitions of {−3,−2,−1, 0, 1, 2, 3}? a) {−3,−1, 1, 3}, {−2, 0, 2} b) {−3,−2,−1, 0},

Home/Math/Which of these collections of subsets are partitions of {−3,−2,−1, 0, 1, 2, 3}? a) {−3,−1, 1, 3}, {−2, 0, 2} b) {−3,−2,−1, 0},

Which of these collections of subsets are partitions of {−3,−2,−1, 0, 1, 2, 3}? a) {−3,−1, 1, 3}, {−2, 0, 2} b) {−3,−2,−1, 0},

Question

Which of these collections of subsets are partitions of {−3,−2,−1, 0, 1, 2, 3}?
a) {−3,−1, 1, 3}, {−2, 0, 2}
b) {−3,−2,−1, 0}, {0, 1, 2, 3}
c) {−3, 3}, {−2, 2}, {−1, 1}, {0}
d) {−3,−2, 2, 3}, {−1, 1}

## Answers ( )

Answer:a) Yes

b)No

c) Yes

d) No

Step-by-step explanation:Remember, a collection of subsets of a set is a partition of if the union of the subsets is , that is, and the elements of are disjoints.

Let

Then

a) and .

Then the collection is a partition of B.

b) and

Since the sets aren’t disjoints then they aren’t a partition of B.

c)

and

Then the elements of the collection are disjoints.

Therefore, is a partition of B.

d) because . Then the collection isn’t a partition of B.