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:

Sleep Terrors

Episodes of screaming, intense fear, and flailing while still asleep, often paired with difficulty fully waking up.

Rapid-eye-movement Sleep

A stage of sleep characterized by movements of the eyes, low muscle tone throughout the body, and the propensity of the sleeper to dream vividly.

Nightmares

Disturbing dreams that can cause feelings of fear, terror, or anxiety, often waking the person from sleep.

Somnambulism

Also known as sleepwalking, it is a disorder that causes people to get up and walk while in a state of sleep.