WAEC 2019 · Paper 2 · Q1

(a)
Draw a table for multiplication $\otimes$ in modulo 8 on the set $T = \{2, 3, 5, 7\}$ .
Show the answer

$\otimes$ 2 3 5 7

2 4 6 2 6

3 6 1 7 5

5 2 7 1 3

7 6 5 3 1
(b)
Use the table to find the solution set of: (i) $3 \otimes n = 5$ ; (ii) $n \otimes n = 1$ .
Show the answer
(i) $\{7\}$ ; (ii) $\{3, 5, 7\}$

Worked solution (try it first)

(a)

Multiply and take the remainder on dividing by 8.
For example $5 \otimes 7 = 35 = 4 \times 8 + 3$ , so the entry is 3.
$\otimes$ 2 3 5 7

2 4 6 2 6

3 6 1 7 5

5 2 7 1 3

7 6 5 3 1

(b)(i)

In the row of 3, the entry 5 is in the column of 7: the solution set is $\{7\}$ .

(ii)

On the diagonal, $n \otimes n = 1$ for $n = 3$ , 5 and 7: the solution set is $\{3, 5, 7\}$ .

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