Identify whether the given pair consists of equal or equivalent but not equal sets or none:
E= set of first five whole numbers.
F = set of first five natural numbers.

Answer

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

### Step 1: Define the Sets
- **Set E**: The set of the first five whole numbers.
- **Set F**: The set of the first five natural numbers.

### Step 2: List the Elements of Each Set
- **Whole Numbers** start from 0, so the first five whole numbers are:
\[ E = \{0, 1, 2, 3, 4\} \]
- **Natural Numbers** start from 1, so the first five natural numbers are:
\[ F = \{1, 2, 3, 4, 5\} \]

### Step 3: Compare the Elements of Both Sets
Now we will compare the elements of sets E and F:
- Set E contains: 0, 1, 2, 3, 4
- Set F contains: 1, 2, 3, 4, 5

### Step 4: Determine if the Sets are Equal
Two sets are equal if they contain exactly the same elements. Here, set E has the element 0, which is not in set F, and set F has the element 5, which is not in set E. Therefore, the sets are **not equal**.

### Step 5: Determine if the Sets are Equivalent
Two sets are equivalent if they have the same number of elements.
- The number of elements in set E is 5.
- The number of elements in set F is also 5.

Since both sets have the same number of elements, they are **equivalent**.

### Conclusion
Sets E and F are **equivalent but not equal**.

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