For Each of the Following Statements, (1) Write the Statement $\forall$

question 4

Essay

For each of the following statements, (1) write the statement informally without using variables or the symbols $\forall$ or $\exists$ , and (2) indicate whether the statement is true or false and briefly justify your answer.
(a) $\forall$ real numbers $x , \exists$ a real number $y$ such that $x < y$ .
(b) $\exists$ a real number $y$ such that $\forall$ real numbers $x , x < y$ .

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Definitions:

Pure Competition

A market structure featuring a large number of small firms selling identical products, with no single firm able to influence market price.

Differentiated Products

Goods and services that are distinct from those offered by competitors due to unique characteristics, branding, quality, or features.

Market Price

The current value at which an asset or service can be bought or sold in an open market.

Firm's Demand Curve

Depicts the relationship between the price of a good or service offered by a firm and the quantity of that good or service consumers are willing and able to purchase.