Use a Quantifier to Make the Following True or False $4 \mathrm { x } = 7 \mathrm { x }$

question 109

Multiple Choice

Use a quantifier to make the following true or false, as indicated, where x is a natural number.
- $4 \mathrm { x } = 7 \mathrm { x }$ (make false)

• A) No natural number \(x\) satisfies \(4 x = 7 x\).
• B) There is no natural number \(x\) such that \(4 x = 7 x\).
• C) For every natural number \(x , 4 x = 7 x\).

---

Definitions:

Response Time

The amount of time it takes for a system or individual to react to a given stimulus or request.

Objective Function

A mathematical formula used in optimization to define the goal that needs to be achieved, usually involving minimization or maximization.

Nonsmooth Optimization

An area of optimization dealing with problems that do not have continuous derivatives, often involving abrupt changes.

Fixed-Cost Problem

An issue in budgeting or economics where costs do not change with the level of production or activity.