Identify the quantifier in the following statements.
There exists a capital city for every state of India.

Answer

To solve the problem of identifying the quantifier in the statement "There exists a capital city for every state of India," we can follow these steps:

### Step 1: Understand the Statement
The statement indicates a relationship between capital cities and states in India. We need to identify the quantifiers used in this context.

### Step 2: Define Variables
Let's define:
- \( x \) as a capital city
- \( y \) as a state of India

### Step 3: Convert the Statement into Symbolic Form
We can express the statement in symbolic form. The phrase "There exists a capital city for every state of India" can be translated as:
- "There exists an \( x \) (capital city) for every \( y \) (state of India)."

This can be written symbolically as:
- \( \exists x \, \forall y \)

### Step 4: Identify the Quantifiers
In the symbolic form \( \exists x \, \forall y \):
- \( \exists \) (there exists) is the existential quantifier, which indicates that there is at least one capital city for the states.
- \( \forall \) (for every) is the universal quantifier, which indicates that this applies to all states of India.

### Step 5: Conclusion
The quantifier in the statement "There exists a capital city for every state of India" is "there exists," which is an existential quantifier.

### Final Answer
The quantifier is "there exists," which is an existential quantifier.

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