Evaluate the following i 5 oplus 2 mod 3 ii 11 ... - SS1 Mathematics Modular Arithmetic Question

Thus, \(- 34\ (mod\ 9)\ \equiv \mathbf{2}\)

1. (i) \(5\ \oplus \ 2\ (mod\ 3)\ \ \ = 7\ (mod\ 3)\)

\(\frac{7}{3} = 2\ remainder\ \mathbf{1}\)

Thus, \(5\ \oplus \ 2\ (mod\ 3)\ \ \ \equiv \mathbf{1}\)

(ii) \(11 \ominus 23\ (mod\ 3) = \ - 12(mod\ 3)\)

\[- 12 = q.3 + x\]

\[- 12 = - 4(3) + x\]

\[- 12 = - 12 + x\]

\(- 12 + 12 = x\)

\[x = \mathbf{0}\]

Thus, \(11 \ominus 23\ (mod\ 3)\ \equiv \mathbf{0}\)

(iii) \(4\ \otimes 16\ (mod\ 4) = 64\ (mod\ 4)\)

\(\frac{64}{4} = 16\ remainder\ \mathbf{0}\)

Thus, \(4\ \otimes 16\ (mod\ 4)\ \equiv \mathbf{0}\)