Determine Whether Each of the Following "Theorems" Is True or False

question 90

True/False

determine whether each of the following "theorems" is true or false. Assume that a, b, c, d,
and m are integers with m > 1.
- $$\text { If } a \equiv b ( \bmod m ) , \text { then } 2 a \equiv 2 b ( \bmod 2 m )$$

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Definitions:

Capitalism

An economic system characterized by private or corporate ownership of goods and services, where production and consumption are driven by market forces and profit motive.

Economic System

An organized way a society structures its economic activities, such as production, distribution, and consumption of goods and services.

Socialism

A political and economic theory advocating for collective or governmental ownership and management of the means of production and distribution of goods.

Classless Society

A society in which hierarchical divisions based on economic status are absent, aiming for equal access to resources and opportunities for all.