Which of the following represents pair of equal sets?

Options

A. `A={1,2,3}, B={x:x in N and x gt 5}`
B. `A={B,O,W,L},B={x:x" is a letter of the word ELBOW"}`
C. `A={1,4,9,16}, B={x:x=n^(2)and 0 lt n lt 5}`
D. `A=phi,B=(O,E,A)`

Answer

To determine which pairs of sets are equal, we need to analyze each given pair of sets and check if they contain the same elements.

### Step-by-Step Solution:

1. **Identify the Sets**:
- **Set A**: {1, 2, 3}
- **Set B**: {x | x ∈ Natural Numbers and x > 5}

2. **Check Equality for Set A and Set B**:
- Set A contains the elements {1, 2, 3}.
- Set B contains elements greater than 5, which are {6, 7, 8, ...}.
- Since the elements of Set A are not present in Set B, **A ≠ B**.

3. **Next Pair of Sets**:
- **Set A**: {b, o, w, l}
- **Set B**: {l, o}

4. **Check Equality for Set A and Set B**:
- Set A contains the elements {b, o, w, l} (4 elements).
- Set B contains the elements {l, o} (2 elements).
- Since the number of elements in both sets is different, **A ≠ B**.

5. **Third Pair of Sets**:
- **Set A**: {1, 4, 9, 16}
- **Set B**: {x | x = n², n > 0 and n < 5}

6. **Check Equality for Set A and Set B**:
- For n = 1, n² = 1
- For n = 2, n² = 4
- For n = 3, n² = 9
- For n = 4, n² = 16
- Thus, Set B contains the elements {1, 4, 9, 16}.
- Since both sets contain the same elements, **A = B**.

7. **Fourth Pair of Sets**:
- **Set A**: {5}
- **Set B**: {0}

8. **Check Equality for Set A and Set B**:
- Set A contains the element {5}.
- Set B contains the element {0}.
- Since the elements are different, **A ≠ B**.

### Conclusion:
The only pair of equal sets is the third pair: **Set A = {1, 4, 9, 16} and Set B = {x | x = n², n > 0 and n < 5}**.