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

question 147

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.
- $$\text { If } a \equiv b ( \bmod 2 m ) \text {, then } a \equiv b ( \bmod m ) \text {. }$$

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Definitions:

Physical Properties

These are characteristics of a substance that can be observed or measured without changing its identity, such as density, color, melting point, and boiling point.

Condensation Point

The temperature at which a gas becomes a liquid; the cooling point where gaseous substances convert into their liquid state.

Alkanes

Hydrocarbons containing only single bonds between carbon atoms, with the general formula CnH2n+2.

Solvents

Substances that dissolve a solute, resulting in a solution; typically liquids but can also be solid or gas.