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Define a binary operation * on the set A={0,1,2,3,4,5} as a*b=a+b (mod 6). Show that zero is the identity for this operation and each element a of the set is invertible with
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SOLVED: Exercise 12.3.6: Thcorem 12.3.5 states that the congruence modulo m rclation is an equivalence rclation (a) Why is 3 = 3 (mod 5)? Hint: Use the definition congruence modulo Prove that
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SOLVED: (2) Let n € N: In Z we define the remainder classes modulo n as [KJn := k+nz:k+m-n:mez for allk €zas well as the relation T3V mod n n teilt 1 -
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