question 11

Essay

$\text { Prove that if } f : X \rightarrow Y \text { and } g : Y \rightarrow Z \text { are one-to-one, then } g \circ f : X \rightarrow Z \text { is also one-to-one. }$

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Definitions:

Qualitative Information

Data that is descriptive in nature, often gathered through methods such as interviews or observations, and not easily reducible to numbers.

Focus Groups

A qualitative research method that involves gathering insights from a small, diverse group of people about their opinions, beliefs, and attitudes towards a product, service, or concept.

Government Mandates

Requirements set by governments that organizations must follow, often related to regulations, safety standards or operational procedures.

Toxic Emissions

Harmful pollutants released into the environment, particularly through processes like manufacturing, automobile exhaust, and energy production.