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Binary Operations — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSBinary Operations3 Marks
Question
Write the multiplication table for the set of integers modulo $5$.
✓

Answer

$Z_5 = {0, 1, 2, 3, 4}$
$a \times _5 b$ is the remainder when the product of $ab$ is divided by $5.$
The composition table for $\times _5$ on $Z_5 = {0, 1, 2, 3, 4}$
$\times _5$ $0$ $1$ $2$ $3$ $4$
$0$ $0$ $0$ $0$ $0$ $0$
$1$ $0$ $1$ $2$ $3$ $4$
$2$ $0$ $2$ $4$ $1$ $3$
$3$ $0$ $3$ $1$ $4$ $2$
$4$ $0$ $4$ $3$ $2$ $1$

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