Are the set `A={b,c,d,e}` and `B={x:x " is a letter in the word 'MASTER'"}` joint?

Answer

To determine if the sets \( A = \{b, c, d, e\} \) and \( B = \{x : x \text{ is a letter in the word 'MASTER'}\} \) are joint (or disjoint), we need to check if they have any elements in common.

### Step-by-Step Solution:

1. **Identify the Elements of Set A**:
- Set \( A \) is given as \( A = \{b, c, d, e\} \).

2. **Identify the Elements of Set B**:
- Set \( B \) consists of the letters in the word "MASTER".
- The letters in "MASTER" are \( M, A, S, T, E, R \).
- Therefore, \( B = \{m, a, s, t, e, r\} \).

3. **Find the Intersection of Sets A and B**:
- The intersection of two sets is the set of elements that are common to both sets.
- We will check each element of set \( A \) to see if it is also in set \( B \):
- \( b \) is not in \( B \).
- \( c \) is not in \( B \).
- \( d \) is not in \( B \).
- \( e \) is in \( B \) (since \( e \) is one of the letters in "MASTER").
- Thus, the common element is \( e \).

4. **Determine if the Sets are Joint (Disjoint)**:
- Since the intersection \( A \cap B = \{e\} \) is not empty (it contains the element \( e \)), the sets are not disjoint.
- Therefore, we conclude that sets \( A \) and \( B \) are not joint sets.

### Conclusion:
Sets \( A \) and \( B \) are not joint sets because they have a common element \( e \).