Consider the direct product of Z2 with Z3, Z2 × Z3. Define the two binary operations as follows: (а, b) @ (с, а) (а, b) 8 (с, d) (а +2С, b +3 d), (а -2 С, b ез d). ie, addition modulo 2 and modulo 3, multiplication modulo 2, and modulo 3, respectively. (Hint: Enumerate the elements of this set.) Prove or disprove that Z2 x Z3 is a field.

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A: x is a positive integer. Find sum of 6x and 11x is divisible by what?

Q: 16. The expansion of (2 + 3x;-1 is valid when >x>

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A: As per Bartleby Guidelines we can solve only one question at a time. Hope you understand

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Q: 2. Let + and · be the usual binary operations of addition and multiplication on the set Z. And let H…

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A: To find the multiplicative inverse of the element 11 in Z138

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A: The detailed solution is given below Thank you

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A: Answer is mentioned below

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A:

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Q: Prove that 6-1 is divisible by 5 for any n 21.

A:

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A:

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A:

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A:

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Q: a1 = 1, an+1 = 3 - An induction method to prove monotor

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A: