If X={S,T,U,V} and Y = {s,t,u,v}, then P and Q are _______ sets. (equal/equivalent)

Answer

To determine whether the sets X and Y are equal or equivalent, we need to analyze the elements of both sets.

### Step-by-Step Solution:

1. **Identify the Elements of Each Set**:
- Set X = {S, T, U, V}
- Set Y = {s, t, u, v}

2. **Count the Number of Elements**:
- Count the elements in Set X: There are 4 elements (S, T, U, V).
- Count the elements in Set Y: There are also 4 elements (s, t, u, v).

3. **Check for Equality**:
- For two sets to be equal, they must contain exactly the same elements.
- Compare the elements of Set X and Set Y:
- Set X has uppercase letters: S, T, U, V.
- Set Y has lowercase letters: s, t, u, v.
- Since the elements are not the same (uppercase vs lowercase), Set X is not equal to Set Y.

4. **Check for Equivalence**:
- For two sets to be equivalent, they must have the same number of elements, regardless of what those elements are.
- Since both sets have 4 elements, they are equivalent.

5. **Conclusion**:
- Therefore, we can conclude that P and Q are equivalent sets.

### Final Answer:
P and Q are **equivalent** sets.