Identify whether the given pair consists of equal or equivalent but not equal sets or none:
C = {x: x ` in N, x + 5 = 6 } and D = {x:x in W, x lt 1 }. `

Answer

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

### Step 1: Define the sets
Set C is defined as:
\[ C = \{ x : x \in \mathbb{N}, x + 5 = 6 \} \]
Set D is defined as:
\[ D = \{ x : x \in \mathbb{W}, x < 1 \} \]

### Step 2: Solve for Set C
We need to find the values of \( x \) that satisfy the equation \( x + 5 = 6 \):
\[ x + 5 = 6 \implies x = 6 - 5 \implies x = 1 \]
Since \( x \) must be a natural number (\( \mathbb{N} \)), we find:
\[ C = \{ 1 \} \]

### Step 3: Solve for Set D
Next, we need to find the whole numbers (\( \mathbb{W} \)) that are less than 1. Whole numbers start from 0 and include all non-negative integers:
\[ D = \{ x : x \in \mathbb{W}, x < 1 \} \]
The only whole number less than 1 is:
\[ D = \{ 0 \} \]

### Step 4: Compare the sets
Now we compare the two sets:
- Set C contains the element \( 1 \).
- Set D contains the element \( 0 \).

Since the elements of the two sets are different, we conclude:
- \( C \neq D \)

### Step 5: Check for equivalence
Next, we check if the sets are equivalent. Two sets are equivalent if they have the same number of elements:
- Set C has 1 element.
- Set D has 1 element.

Since both sets have the same number of elements, we conclude:
- \( C \) and \( D \) are equivalent.

### Final Conclusion
The sets C and D are equivalent but not equal.

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