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Identify the quantifier in the following...

Identify the quantifier in the following statement :
"For all real numbers x and y, xy=yx"

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To identify the quantifier in the statement "For all real numbers x and y, xy = yx," we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Statement**: The statement asserts that for any real numbers x and y, the product of x and y is equal to the product of y and x. This is a property of multiplication known as the commutative property. 2. **Identify the Key Phrase**: Look for phrases in the statement that indicate the scope of the assertion. In this case, the phrase "For all real numbers x and y" indicates that the statement applies universally to all real numbers. 3. **Define Quantifiers**: A quantifier is a word or phrase that indicates the quantity of subjects to which the statement applies. Common quantifiers include "for all," "there exists," "for every," etc. 4. **Locate the Quantifier**: In the statement, the phrase "For all" is the key part that indicates the universal nature of the assertion. It tells us that the statement is true for every possible pair of real numbers x and y. 5. **Conclude the Identification**: Since "For all" is the phrase that quantifies the statement regarding the real numbers, we can conclude that the quantifier in the statement is "For all." ### Final Answer: The quantifier in the statement "For all real numbers x and y, xy = yx" is **"For all."**
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