The number of sets X, such that `X sube A and X notsube B` , where `A = {a, b, c, d, e), B = (c, d}`

Options

A. 26
B. 27
C. 28
D. 29

Answer

To solve the problem of finding the number of sets \( X \) such that \( X \subseteq A \) and \( X \not\subseteq B \), where \( A = \{a, b, c, d, e\} \) and \( B = \{c, d\} \), we can follow these steps:

### Step 1: Determine the total number of subsets of set \( A \)

Set \( A \) has 5 elements: \( \{a, b, c, d, e\} \). The total number of subsets of a set with \( n \) elements is given by \( 2^n \).

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

### Step 2: Determine the total number of subsets of set \( B \)

Set \( B \) has 2 elements: \( \{c, d\} \). Using the same formula for the number of subsets:

\[ \text{Total subsets of } B = 2^2 = 4 \]

### Step 3: Identify the subsets of \( A \) that are also subsets of \( B \)

The subsets of \( B \) are:
1. \( \emptyset \)
2. \( \{c\} \)
3. \( \{d\} \)
4. \( \{c, d\} \)

### Step 4: Calculate the number of subsets of \( A \) that are not subsets of \( B \)

To find the number of sets \( X \) that are subsets of \( A \) but not subsets of \( B \), we subtract the number of subsets of \( B \) from the total number of subsets of \( A \):

\[ \text{Number of subsets of } A \text{ not in } B = \text{Total subsets of } A - \text{Total subsets of } B \]
\[ = 32 - 4 = 28 \]

### Conclusion

The number of sets \( X \) such that \( X \subseteq A \) and \( X \not\subseteq B \) is \( 28 \).

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