Which of the following is true?

Options

A. `A={1,7,6}` and `B={7,2,1}` then `1,2,7 in A`.
B. `A={a,b,c}` and `B={b,c,d}` then `a,b,c in B`.
C. `A={a,e,i,o,u}` and `B={a,b,c,d,….,x,y,z}` then `a,e,i,o,u in B`,
D. `A={1,2,1,2}` and `B={a,b,c}` then, `1,2 in B`

Answer

To solve the question "Which of the following is true?" we will analyze each option provided to determine its validity.

### Step-by-Step Solution:

1. **Option 1:**
- Let \( A = \{1, 7, 6\} \) and \( B = \{7, 2, 1\} \).
- We need to check if \( \{1, 2, 7\} \in A \).
- The set \( A \) contains the elements 1, 7, and 6. The element 2 is not in \( A \).
- Therefore, \( \{1, 2, 7\} \notin A \) is **false**.

2. **Option 2:**
- Let \( A = \{A, B, C\} \) and \( B = \{B, C, D\} \).
- We need to check if \( \{A, B, C\} \in B \).
- The set \( B \) contains the elements B, C, and D. The element A is not in \( B \).
- Therefore, \( \{A, B, C\} \notin B \) is **false**.

3. **Option 3:**
- Let \( A = \{A, E, I, O, U\} \) (the set of vowels) and \( B = \{A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z\} \) (the set of all alphabets).
- We need to check if \( \{A, E, I, O, U\} \in B \).
- The set \( B \) contains all the alphabets, which includes A, E, I, O, and U.
- Therefore, \( \{A, E, I, O, U\} \in B \) is **true**.

4. **Option 4:**
- Let \( A = \{1, 2, 1, 2\} \) (which simplifies to \( \{1, 2\} \)) and \( B = \{A, B, C\} \).
- We need to check if \( \{1, 2\} \in B \).
- The set \( B \) contains the elements A, B, and C, none of which are the same as \( \{1, 2\} \).
- Therefore, \( \{1, 2\} \notin B \) is **false**.

### Conclusion:
The only true statement is from **Option 3**: \( A, E, I, O, U \in B \).