Question

How many proper subsets does the set l, metric units of length, have? l={ mm, cm, m, km }

Answer 1

D)15

Step-by-step explanation:

Given a set A, a proper subset of A is any subset of A that is not equal to A.

If a set has n elements, the total number of subsets of the set will be:

In the given set:

Therefore, the number of proper subsets of the given set will be:

Answer 2

The set of metric units of length {mm, cm, m, km} has 15 proper subsets, calculated using the formula 2^n - 1, where n is the number of elements in the set.

Step-by-step explanation:

The question relates to the concept of proper subsets in the mathematics field, more specifically combinatorics, which deals with counting and arrangements of elements within sets. A proper subset of a set is any subset that is not equal to the set itself, which means it can contain some or none of the elements, but not all of them. To determine the number of proper subsets for the set l, consisting of the metric units of length: {mm, cm, m, km}, we use the formula 2n - 1 where n is the number of elements in the set. The set l has 4 elements, so it will have 24 - 1 which equals 15 proper subsets.