D. Define the multiplication operation * as modulo 10 in G = {1, 3, 5, 7,}. Cr table for this. Verify the theorem (a * -b)- = b-1+ a-1. 1. (7 5)-1 2. 5-1+7-1

Q: Find the number of elements in the conjugacy class of (abc)(def) in S₆

A: We have to find the number of elements in the conjugacy class of (a b c)(d e f) in S₆

Q: * For each integer n, let Cn = {n²,n³, nª}. How many elements are in each of C-2, C-1, Co, and C3?…

A: The set always contains the distinct elements. Given Cn = n2 , n3 , n4 Consider C-2 = (-2)2 , (-2)3…

Q: (7) (a) Find the order of a modulo 7 for a = 1, 2, 3, 4, 5, 6.

A:

Q: 7. The heights reached by 15 model rockets launched by the students in Mr. Fiori's science class are…

A: The main objective of this question is, by using the stem leaf plot we need to provide minimum and…

Q: Find all Pnterers x such that 5x=12 (mat) LoxE 4 (mad) 7x=16 (modlo) and 1o00s x3000

A:

Q: A) Let m=7. How do you find the inverse of all integers from 1 through 6 using the multiplication…

A:

Q: Q5/Find the addition result for the following operation (66)8+ (1100)EX-3+(83)10- (F2.1)16 using 2's…

A: Solution :-

Q: Test2

A: We know that2198=2128×264×24×22Also we have22≡4(mod 397)24≡16(mod 397)28≡256(mod…

Q: 1 101101, and 101, 2. 10111102 and 102 and 112 3. 1000012

A: Since there are multiple questions the first question is answered as per our guidelines. Kindly…

Q: Find the least residue of  -5 -46 modulo 14.

A:

Q: 24. Give a recursive definition of a) the set of odd positive integers. b) the set of positive…

A:

Q: 2. Euclidean Algorithm Use the Euclidean algorithm to find gcd(12345, 678).

A: We need to find the GCD(12345,678)=?

Q: p Pq C N-n N-1

A:

Q: (b) Find 95! (mod 96).

A: We have to find the value of 95!(mod 96). Since 95!=95*94*93*…*8*7*6*5*4*3*2*1.

Q: Match each of the following integers with its equivalent representation in a different base. (123) g…

A: Number system are of the type  Binary decimal with two bits 0 or 1. The decimal number is from 0 to…

Q: x² + 4x = 10(mod11) (mod11) X=

A: Given that x2+4x≡10 (mod 11)x2+4x+4≡10+4 (mod 11)x2+4x+4≡14 (mod 11)x2+4x)(x+2)2≡14+11 (mod…

Q: Solve for X, show all calculation in binary number system only X = ((1110)₂-(0011)₂) (10011010)₂)…

A:

Q: Hellcopter Trip Whale Watching Adventure Volcano Tour Hours Cost ($) Hours Cost ($) Hours Cost ($)…

A: We can use linear equations to solve these types of problems. There are different methods available…

Q: x² + x = 13(mod17) X= * (mod17)

A:

Q: x² - 2x = 8(mod19) X= (mod19)

A:

Q: 2. Create the following tables: (a) Addition table for modulo 7 (b) Multiplication table for modulo…

A:

Q: What is the inverse of 16 modulo 43 i.e. which number a has the property that 16*a has the remainder…

A: From question we have to find the inverse of 16 modulo 43. i.e  16*a mod(43)=1 It can also be…

Q: Sort this permutation [5 213 4] into identity permutation [123 4 5]. Check what's the number number…

A: The permutation is nothing but the arrangement of objects in different orders. If we permute a set…

Q: For each of the following pairs, determine whether they are congruent modulo (b) 132 and 10 11.…

A: Given below the detailed solution

Q: One of the striking properties of Fibonacci numbers is that gcd(Fm, Fn) = Fd, (*) where d = gcd (m,…

A: 1. We see,        F9 = 34    [Fibonacci series : 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,. . . . . ]…

Q: 4. Does 3 divide (3k + 1)(3k + 2)(3k + 3)?

A: We will show by induction, put the value of k = 0 we find, (3x0+1)(3x0+2)(3x0+3) = 6  Which is…

Q: Find the order of 4 modulo 49.

A: Evaluate order of 4 modulo 49.

Q: Q4/ Find the element of GF(2³) then by using the multiplication table find (x+1)-¹ mod (x² + x + 1).…

A:

Q: Use induction to show that 12 -7 is divisible by 5.

A:

Q: If 3x = 6 mod 9, when -2 <x< 8. Then O x=(-1, 3, 5} x=(-1, 2, 5} O x=(-1, 2, 3} O x=(-1, 5, 6}

A:

Q: Let the binary operation *

A: Given,          a*b=a+2b where a and b are real numbers

Q: 7*11*13*15+15 is a _

A: From the given problem:   7×11×13×15+15   As we know that the order of mathematical operations is:…