ted +n; the second will resemble ordinary multiplication and be De denoted Xn DEFINITION 4.7. Given p, q E {0, 1, 2, - . ,n – 1}, define: i) p +n q to be the remainder when p+q is divided by n, and ii) p Xn q to be the remainder when p x q is divided by n. These operations are referred to as addition mod(n) and multiplication mod(n), respectively. ACTIVITY 4.21. Use the above definitions to calculate each of the following in the set Z12. (a) 3+12 6 (b) 8 +12 7 (c) 3 x12 6 (d) 8 x12 7 -...pdf

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A: Since you have uploaded multiple questions according to our guidelines we have solved first question…

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A: (d) For all integers a and b, if ab=7 mod 12, then either a =1 mod 12 or a =7 mod 12

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.