2.3.2 Dial Pad Relation

Types: N/A
Examples: N/A
Constructions: N/A
Generalizations: 2.3 Relation, 2.4 Domain, Range, & More

Properties: N/A
Sufficiencies: N/A
Questions: N/A

Dial Pad Relation

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Let

\begin{aligned} U & = {A, B, C, \dots, Z} \\ N & = {0, 1, 2, \dots, 9} \\ N \times U & = \begin{array}{c} { & (0, A), & (0, B), & (0, C), & (0, D), & (0, E), & \dots, & (0, Z), \\ (1, A), & (1, B), & \dots, & (9, Z) & } \end{array} \end{aligned}

Solution. The relation for the dial pad would be:

R = \begin{matrix} { & (2, A), & (2, B), & (2, C), & (3, D), & (3, E), \\ \dots, & (9, W), & (9, X), & (9, Y), & (9, Z) & } \end{matrix}

This relation is valid because $R \subseteq N \times U$ .

Domain & Range of Dial Pad Relation

Find the domain and range of the dial pad relation from Example I.

Looking back at the "Dial Pad" relation, we see:

\begin{aligned} Domain Space (D) & = N = {0, 1, 2, 3, \dots, 9} \\ Dom (D) & = {2, 3, 4, 5, \dots, 9} & Notice how 0 and 9 are unused \\ Codomain (D) & = U \\ Rng (D) & = U \end{aligned}

In this case, $U$ represents the set of upper case letters in the English alphabet.