(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: How can I prove that Z4 is cylic? I know that It has something to do with generators (I think?) and…

A: We have a group Z4. We have to prove that Z4 is cyclic.

Q: (c) 2, 3, 4+ V10 and 4. V10 are irreducible elements of R.

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Q: Compute the following: (a) 4!, (b) (), (c) (₂), (d) (), (e) (7), (f) (2)-(2) where n is a…

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Q: 5) Expand using special product rules c) (12 – 4x)? d) (3y – 6)2

A: c. Given: Apply special product rule in the above expression.

Q: Consider the sum (3)² + (8)² + (13)2 + · . + (15n – 2)2. | m 1 1 m(т + 1)] and k2 = (m(m + 1)(2m +…

A: Consider S=32+82+132+ . . . .+15n-22

Q: Let gcd(a, b) = d then which of the following is correct (i) dla (ii) dlb (iii) d(ax + by) (a) only…

A: The correct option is option (d) all the three.    The detailed explanation is as follows below :

Q: Show that (p-1)(p2) (pr) (-1)'r!(mod p), for r= 1, 2, . . . ,p - 1. .

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Q: What is the output of the given circuit? Irverter OR gate AND gate O a l-qn(qmp)]^(qvp) O b.…

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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: 4. Let gcd(a, b) = d then which of the following is correct (a) d = ab (b) (ax + by)|d (c) d[(ax +…

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Q: :: Find L-1 5+7 \s+7/

A:

Q: Which of the following is equivalent to - (Vx (P(x)VQ (x?),

A: we will use demorgan law here 1)   ∼(P∧Q)=(∼P)∨(∼Q) 2)  ∼(P∨Q)=(∼P)∧(∼Q)

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: When an (1) 3 2 ak+1 = -3ak +2 (k=1,2,3...), a₁ = (1) × [(2)″ +(3) (2) (3)

A: To determine the missing terms in the following.When a1=32ak+1=-3ak+2         k=1, 2, 3, ...,…

Q: 7. 2) Write the difference equation for the systems shown below. ii) Find yon) / xen). yon) x(n) 3…

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Q: (d) (27+5)(2- i)|=/3 12z +5|. %3D

A: Solution D: We have to prove (2z¯+5)(2-i)=3(2z+5) L.H.S. Let z=x+iy So z¯=x-iy therefore…

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…

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Q: 5. Show that n²(7n – 2) is O(n³).

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Q: [2 Define A = 1 -2 Lo ܚ ܨܢ ܝܪ -12 31 5 0 -2 -2 1. Evaluate, showing your work: (i) B = (ii) (iii)…

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Q: The 4th term in the expansion of (2x -3x 10 is 10 C4 (2a) (-3x)³ O 10 C4 (2a2) (-32)4 10 C (2)…

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Q: 5. Find LU Factorizatioon of A = [5 2 1 1 3 2 7 1 2 3 2 1- Show the work!

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

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Q: Let gcd(a, b) = d then which of the following is correct (i) dla (ii) d|b (iii) d[(ax + by) (a) only…

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

A: