 find number of proper subset of set S is equals to ( 1 2 3)

To find the number of **proper subsets** of a set \( S = \{1, 2, 3\} \), follow these steps:

### Step 1: Total number of subsets
For a set with \( n \) elements, the total number of subsets (including the empty set and the set itself) is given by:
\[
2^n
\]
In this case, \( n = 3 \) (since the set \( S \) has three elements), so the total number of subsets is:
\[
2^3 = 8
\]

### Step 2: Proper subsets
A **proper subset** is any subset of a set that is not equal to the set itself. To find the number of proper subsets, we subtract 1 (since the set itself is not considered a proper subset):
\[
\text{Number of proper subsets} = 2^n - 1 = 8 - 1 = 7
\]

So, the number of proper subsets of the set \( S = \{1, 2, 3\} \) is **7**.

Would you like further details or have any questions?

Here are five related questions:
1. What are the proper subsets of the set \( S = \{1, 2, 3\} \)?
2. How many subsets does a set with 4 elements have?
3. What is the difference between a subset and a proper subset?
4. How does the formula for the number of subsets work for an empty set?
5. Can a set be a subset of itself?

**Tip**: The total number of subsets of a set doubles with each additional element because each element has two possibilities: being included or excluded.

find number of proper subset of set S is equals to ( 1 2 3)

Learn how to find the number of proper subsets of the set S = {1, 2, 3}. This problem covers fundamental set theory concepts, including how to calculate total and proper subsets using the formula 2^n - 1. Suitable for students in Grades 5-7.

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