Identify the quantifier in the following and state its type `:`
For every `x in N , x + 3` is greater than x.

Answer

To solve the problem, we need to identify the quantifier in the given statement and determine its type. The statement provided is:

"For every \( x \in \mathbb{N} \), \( x + 3 \) is greater than \( x \)."

### Step-by-Step Solution:

1. **Identify the Quantifier**:
- The phrase "For every" indicates that we are referring to all elements within a certain set. In this case, the set is the natural numbers \( \mathbb{N} \).
- Therefore, the quantifier in this statement is "for every \( x \)".

2. **Determine the Type of Quantifier**:
- There are two main types of quantifiers:
- **Universal Quantifier**: This is used to state that a property holds for all elements in a particular set. It is often represented by the phrase "for all" or "for every".
- **Existential Quantifier**: This indicates that there exists at least one element in the set for which the property holds. It is represented by phrases like "there exists".
- Since the phrase "for every" is used in our statement, it falls under the category of the Universal Quantifier.

3. **Conclusion**:
- The quantifier identified is "for every \( x \)".
- The type of this quantifier is Universal Quantifier.

### Final Answer:
- Quantifier: "for every \( x \)"
- Type: Universal Quantifier