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Identify the quantifier in the following...

Identify the quantifier in the following and state its type `:`
There exists `x in N , x + 3 =9`.

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To solve the problem, we need to identify the quantifier in the statement "There exists x in N, x + 3 = 9" and state its type. ### Step-by-Step Solution: 1. **Identify the Statement**: The given statement is "There exists x in N, x + 3 = 9". 2. **Locate the Quantifier**: In this statement, the phrase "There exists" indicates the presence of a quantifier. 3. **Determine the Type of Quantifier**: - There are two main types of quantifiers: - **Universal Quantifier**: Denoted by "for all" (∀), which indicates that a statement is true for every element in a particular set. - **Existential Quantifier**: Denoted by "there exists" (∃), which indicates that there is at least one element in a set for which the statement is true. - In our statement, "There exists" corresponds to the existential quantifier. 4. **Conclusion**: Therefore, the quantifier identified is "There exists" and its type is an **existential quantifier**. ### Final Answer: - **Quantifier**: There exists - **Type**: Existential quantifier
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