State, whether the following pairs of sets are equivalent or not:
Set of whole numbers and set of multiples of 3.

Answer

To determine whether the set of whole numbers and the set of multiples of 3 are equivalent, we need to analyze the elements in each set and their cardinality (the number of elements in each set).

### Step 1: Define the sets
- The **set of whole numbers** is defined as:
\[ W = \{0, 1, 2, 3, 4, 5, \ldots\} \]
This set includes all non-negative integers starting from 0 and goes on to infinity.

- The **set of multiples of 3** is defined as:
\[ M = \{0, 3, 6, 9, 12, 15, \ldots\} \]
This set includes all integers that can be expressed as \(3n\) where \(n\) is a non-negative integer.

### Step 2: Count the elements in each set
- The set of whole numbers \(W\) has an infinite number of elements.
- The set of multiples of 3 \(M\) also has an infinite number of elements.

### Step 3: Determine if the sets are equivalent
- Two sets are considered equivalent if they have the same cardinality, meaning they contain the same number of elements.
- Although both sets have an infinite number of elements, we need to analyze the nature of their infinity. The set of whole numbers contains all non-negative integers, while the set of multiples of 3 contains only those integers that are multiples of 3.

### Step 4: Conclusion
- The cardinality of the set of whole numbers is greater than the cardinality of the set of multiples of 3. Therefore, the two sets are **not equivalent**.

### Final Statement
Thus, the set of whole numbers and the set of multiples of 3 are not equivalent.

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