Let $X = \{ 1,2,3,4,5 \}$ And $Y = \{ u , v , w , x , y \}$

question 13

Essay

Let $X = \{ 1,2,3,4,5 \}$ and $Y = \{ u , v , w , x , y \}$ , and define $h : X \rightarrow Y$ as follows:
$h ( 1 ) = v , h ( 2 ) = x , h ( 3 ) = v , h ( 4 ) = v , h ( 5 ) = y .$
(a) Draw an arrow diagram for $h$ .
(b) Let $A = \{ 1,2 \} , C = \{ x , v \} , D = \{ w \}$ , and $E = \{ w , y \}$ . Find
$$h ( A ) , h ( X ) , h ^ { - 1 } ( C ) , h ^ { - 1 } ( D ) , h ^ { - 1 } ( E ) , \text { and } h ^ { - 1 } ( Y ) .$$

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Definitions:

Taste

One of the five senses, it is the perception of flavor perceived in the mouth and throat on contact with a substance.

Olfaction

The sense of smell, an important sensory system allowing for the detection and identification of odors in the environment.

Audition

The sense of hearing; the perception of sound.

Vestibular Sense

A sensory system responsible for providing our brain with information about motion, head position, and spatial orientation; it also helps with balance and eye movements.