Identify the quantifier in the following statements and write the negation of the statements.
For every real numbers x,x is less than x+1.

Answer

To solve the problem, we need to identify the quantifier in the given statement and then write its negation.

**Step 1: Identify the quantifier.**

The statement given is: "For every real number x, x is less than x + 1."

In this statement, the quantifier is "for every." This indicates that the statement applies to all real numbers x.

**Step 2: Write the negation of the statement.**

The negation of a statement that uses a universal quantifier (like "for every") can be expressed by changing it to an existential quantifier (like "there exists").

The original statement can be rewritten as:
- "For every real number x, x < x + 1."

To negate this, we say:
- "It is not true that for every real number x, x < x + 1."
This can be expressed as:
- "There exists a real number x such that x is not less than x + 1."

In mathematical notation, the negation can be written as:
- "There exists a real number x such that x ≥ x + 1."

**Final Answer:**
- Quantifier: For every
- Negation: There exists a real number x such that x ≥ x + 1.

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