(8) In the ring (Z,, +6,•6 ), we get n {(a): a prime element in Zg} ...... (а) ф (b) ((0), +6, ·6 ) (c) (Z6, +6,-6) (d) No Choice (a) O (b) O (c) (d)

Q: (2-1)

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Q: Prove the following: (a) If a, b,c € Z+ and a+b=c then (c, [a, b]) = (a, b).

A: As per bartleby guidelines for more than one questions asked only first should be answered. Please…

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A: Using the property of inner product. In question #2 , if the metric is induced by inner product then…

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Q: (1) (A × B) U (B × C) (2) AX (BUC) C = {9,10}, B = {7,8} , A = {4,5}

A:

Q: 2х1 + 3х, — хз — 2 Зх1 — 2х2 + хз — —1 = -1 — 5х1 — 4х2 + 2xз — 3

A: Given that  The system of equations  To find the solution of system of equations by using cramers…

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Q: Q:- Show thet B(n, n) B( n+on+=2 1-40

A: The solution is given as

Q: (10) The following element is prime in (Ze,+,.) = .... .. (а) 2 (b) 4 (c) 12 (d) No Choice (а) (b)…

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Q: (2n)!6" (Зп)!) (-5)1+ 5n-3 Σ (2n+7)3

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Q: (7- 8)2 | /8-ん (e-)」ade-)|I/8-ん Hence, 2By < 1, (7 – 6)2 vhich can be written as |a(y – 8) + 3||y –…

A: I have only deducted the green part as per your request.

Q: Value of the 7th term in (2x + y)"?

A: Follow the procedure given below.

Q: What is the result of the following operation: (1,10) n (10) (A) 0 B) (1,10) (1,10) (1,10)

A: We have to find the intersection The intersection of two sets is the set of elements that are common…

Q: 2. (i) (1 2 3 4 5) (2 5 4 3 1) and (1 5 3 2 4) Find the product of the permutations: (a, az ... Ax)…

A: NOTE- Since the terms in the last bracket of first part are not clear, so solving just second part…

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A:

Q: Use a combinatorial argument to prove that EC(n, k) = 2". k=0

A: The Multiplication Principle If one event can occur in m ways and a second event can occur in n ways…

Q: 36 6 10. Find the coefficient of x³6 in (x + x² + x³ + x² + x³ + x² + x² + x³) ³

A: To find the coefficient of the term x36 in the expansion of x+x2+x3+x4+x5+x6+x7+x85.

Q: If In(a) = 2, In(b) = 3, and In(c) = 5, evaluate the following: %3D ) a-1 (a) In -12 b-3c-1 (b) In…

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Q: n2 1 SHOW ALL OF YOUR WORK. 3. an = 2n +1 2n + 1" (а) Find aj, а2, аз, а4. 3 (b) Compute > a;. i=1 4…

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Q: Consider the truth table for the connective '' with two simple declarative statements p and q. Р q T…

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Q: (x-1)2 (y+2)? What are the endpoints of the conjugate axis of 25 - 36 O (1 ± 5, –2) O (1, -2 ± 6) O…

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Q: (a) If a, b,c € Z+ and a +b=c then (c,[a, b)) = (a, b).

A: As you asked multiple questions , so I solved only the first one.

Q: (1 2 43) 32 1. IF A = THEN (A) (B) (X Y) Z W

A:

Q: (5) {1,2} C P({1, 2}).

A: Given  set is {1,2},  we knew that power set of a given set is set of all subsets of the given set.…

Q: 11| Q1) If A--2 -1,B 3 3 4 -5 -1 -1 13 -1 Find (–1 x A) + (B + C)

A:

Q: Show that (6+c) ba са (c+a) cb =2abc(a+b+c) ab 3 (a+b) ас bc

A:

Q: 4[(b+f)-(c+r)][a (d+g)-(e+s)][(c+r)(d+g)+a(e+s)(b+f)] [((e+s) – (d+g))(a+1)] K ae ([(b+ f) – c] +…

A: Given, x1-Q=a(d+g)-(e+s)b+f-c+rc+rd+g+ae+sb+fa(e+s)…

Q: 2. Let A = - (37 (c) BC (d) CA (e) AAT (0 n B = Evaluate the following products: (a) AB (b) A² C= 3…

A: We are given with the multiple number of subparts answer according to the guudeline

Q: Factor 10+ 4i into product of primes Z [i], (Hint: Ille= (2)(2)(29)) in %3D

A: