Question
Question 6 Given a set \( \mathrm{A}=\{m, n, I, G, 5\} \), answer the following questions: a. Find the number of subsets of A b. Find the number of proper subsets of A Check Answer
Ask by Munoz Brewer. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
There are 32 subsets of set A and 31 proper subsets of set A.
Solution
1. Since set \( \mathrm{A} \) has 5 elements, the total number of subsets is given by:
\[
2^5 = 32.
\]
2. A proper subset is any subset of \( \mathrm{A} \) that is not equal to \( \mathrm{A} \) itself. Thus, we subtract 1 (which corresponds to the subset that is \( \mathrm{A} \) itself) from the total number of subsets:
\[
2^5 - 1 = 32 - 1 = 31.
\]
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Simplify this solution The Deep Dive
To find the number of subsets of a set \( \mathrm{A}=\{m, n, I, G, 5\} \), we can use the formula \( 2^{n} \), where \( n \) is the number of elements in the set. Since \( \mathrm{A} \) has 5 elements, the number of subsets is \( 2^{5} = 32 \). For the number of proper subsets, we take the total number of subsets and subtract 1 (to exclude the set itself). Thus, the number of proper subsets is \( 32 - 1 = 31 \). So the answers are: a. 32 subsets b. 31 proper subsets
