To analyze whether the given statements about the sets $ A $ and $ B $ are true, we will break down the problem as follows:

### 1. Break Down the Problem
We need to analyze the relationships between sets $ A $ and $ B $. We will consider each proposed answer to see if they hold true.

### 2. Relevant Concepts
- **Set Membership**: A set $ X $ is said to be a subset of set $ Y $ (denoted as $ X \subseteq Y $) if every element of $ X $ is also an element of $ Y $.
- **Set Equality**: Two sets $ X $ and $ Y $ are equal (denoted as $ X = Y $) if they contain exactly the same elements.

### 3. Analysis and Detail
- **Sets**:
Let $ A = \{a, b, c, d, e, f\} $
Let $ B = \{\{a, b, c, d, e, f\}, \{1,2,3\}\} $

- Examining $ A $: It contains the elements $ a, b, c, d, e, f $.
- Examining $ B $: It contains two elements: $ \{a, b, c, d, e, f\} $ and $ \{1, 2, 3\} $.

1. **Is $ A \subseteq B $?**
No, set $ A $ is not a subset of $ B $ because the individual elements of $ A $ (like $ a $) are not found in $ B $ itself; instead, $ B $ contains the set $ A $ as one of its members.

2. **Is $ B \subseteq A $?**
No, $ B $ is not a subset of $ A $ because $ B $ contains sets $ \{a, b, c, d, e, f\} $ and $ \{1, 2, 3\} $, which are not elements of $ A $.

3. **Is $ A = B $?**
No, the sets $ A $ and $ B $ are not equal since $ A $ contains members that are individual elements while $ B $ contains other sets.

4. **Is $ A \supseteq B $?**
No, $ A $ does not include all elements of $ B $.

5. **Is $ B \supseteq A $?**
No, $ B $ does not include all elements of $ A $ because the individual elements of $ A $ are not in $ B $.

### 4. Verify and Summarize
Upon analyzing all options, it is clear that none of the relationships indicated by the statements are true. Thus:

### Final Answer
None of the following statements are true:
- a. $ A \subseteq B $
- b. $ B \subseteq A $
- c. $ A = B $
- d. $ B \subseteq A $
- e. $ A \supseteq B $

Therefore, all proposed answers regarding the relationships between $ A $ and $ B $ are false.

Question

To analyze whether the given statements about the sets $ A $ and $ B $ are true, we will break down the problem as follows:

### 1. Break Down the Problem
We need to analyze the relationships between sets $ A $ and $ B $. We will consider each proposed answer to see if they hold true.

### 2. Relevant Concepts
- **Set Membership**: A set $ X $ is said to be a subset of set $ Y $ (denoted as $ X \subseteq Y $) if every element of $ X $ is also an element of $ Y $.
- **Set Equality**: Two sets $ X $ and $ Y $ are equal (denoted as $ X = Y $) if they contain exactly the same elements.

### 3. Analysis and Detail
- **Sets**:  
  Let $ A = \{a, b, c, d, e, f\} $  
  Let $ B = \{\{a, b, c, d, e, f\}, \{1,2,3\}\} $
  
  - Examining $ A $: It contains the elements $ a, b, c, d, e, f $.
  - Examining $ B $: It contains two elements: $ \{a, b, c, d, e, f\} $ and $ \{1, 2, 3\} $.

1. **Is $ A \subseteq B $?**  
   No, set $ A $ is not a subset of $ B $ because the individual elements of $ A $ (like $ a $) are not found in $ B $ itself; instead, $ B $ contains the set $ A $ as one of its members.

2. **Is $ B \subseteq A $?**  
   No, $ B $ is not a subset of $ A $ because $ B $ contains sets $ \{a, b, c, d, e, f\} $ and $ \{1, 2, 3\} $, which are not elements of $ A $.

3. **Is $ A = B $?**  
   No, the sets $ A $ and $ B $ are not equal since $ A $ contains members that are individual elements while $ B $ contains other sets.

4. **Is $ A \supseteq B $?**  
   No, $ A $ does not include all elements of $ B $.

5. **Is $ B \supseteq A $?**  
   No, $ B $ does not include all elements of $ A $ because the individual elements of $ A $ are not in $ B $.

### 4. Verify and Summarize
Upon analyzing all options, it is clear that none of the relationships indicated by the statements are true. Thus:

### Final Answer
None of the following statements are true:
- a. $ A \subseteq B $
- b. $ B \subseteq A $
- c. $ A = B $
- d. $ B \subseteq A $ 
- e. $ A \supseteq B $

Therefore, all proposed answers regarding the relationships between $ A $ and $ B $ are false.

Knowee AI · Accepted Answer