Identify whether the given pair consists of equal or equivalent but not equal sets or none:
G= {a,b,c} and H={x,y,z}

Answer

To determine whether the sets G and H are equal, equivalent but not equal, or neither, we will follow these steps:

### Step 1: Define the Sets
We have two sets:
- Set G = {a, b, c}
- Set H = {x, y, z}

### Step 2: Check for Equality
Two sets are considered equal if they contain exactly the same elements.
- In this case, G contains the elements {a, b, c} and H contains the elements {x, y, z}.
- Since the elements in G are not the same as the elements in H, we conclude that G is not equal to H.

### Step 3: Check for Equivalence
Two sets are considered equivalent if they have the same number of elements, regardless of what those elements are.
- Count the number of elements in each set:
- Set G has 3 elements: {a, b, c}
- Set H also has 3 elements: {x, y, z}
- Since both sets have the same number of elements (3), we conclude that G and H are equivalent.

### Final Conclusion
- G and H are equivalent sets but not equal sets.

### Summary
- G and H are equivalent sets.

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