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### Problem Summary:
We are given the set \( A = \{17, 19, 31, 37, 43\} \). The task is to:
(a) Find the total number of proper subsets of \( A \).  
(b) Find the total number of subsets of \( A \).

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### Solution:

#### (b) Total number of subsets of \( A \):
The formula to find the total number of subsets of a set with \( n \) elements is:

\[
\text{Total subsets} = 2^n
\]

Here, \( n = 5 \) (since \( A \) has 5 elements). Therefore:

\[
\text{Total subsets} = 2^5 = 32
\]

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#### (a) Total number of proper subsets of \( A \):
A **proper subset** is any subset of \( A \) that is not equal to \( A \) itself. The number of proper subsets is:

\[
\text{Proper subsets} = \text{Total subsets} - 1
\]

This is because we exclude the set \( A \) itself from the total subsets. So:

\[
\text{Proper subsets} = 32 - 1 = 31
\]

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### Final Answers:
(a) Total number of proper subsets of \( A \): **31**  
(b) Total number of subsets of \( A \): **32**

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Would you like further explanation or details on subsets and proper subsets?  

Here are five related questions for practice:
1. What is the total number of subsets of a set with \( n = 6 \) elements?
2. How many proper subsets does a set with \( n = 7 \) elements have?
3. What is the difference between a proper subset and a subset?
4. Can an empty set be a proper subset of any set? Why?
5. If a set has \( n = 10 \) elements, how many subsets and proper subsets does it have?

**Tip**: To find subsets quickly, remember that the total subsets grow exponentially with the size of the set: \( 2^n \).

Let the set A be defined as A = {17, 19, 31, 37, 43}. Find (a) the total number of proper subsets of A, and (b) the total number of subsets of A.

Learn how to calculate the total number of subsets and proper subsets of a set. This example uses the set A = {17, 19, 31, 37, 43}, explaining concepts in set theory and the formula 2^n for subsets. Perfect for Grades 9-12.

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