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7. Prove or disprove: If we know that 2X +6=4 (mod 8), then X +3 =...
Please answer the parts 6 and 7. Thank you. 2. In this problem, we will prove the following result: If G is a group of order 35, then G is isomorphic to Zg We will proceed by contradiction, so throughout the following questions, assume that G is a group of order 35 that is not cyclic. Most of these questions can he solved independently I. Show that every element of G except the identity has order 5 or 7. Let...
Q4 Let z = dkdk-1 d2dı be the base 10 representation of an integer x where di,..., dk are digits drawn from 0,...,9. Explain why x d1 + d2 + . . . + dk (mod 9) = so, also, z di + d2 + . . . + dk (mod 3) = and Thus for example to check whether 57,711 is divisible by 9 or 3 we just add up the digits 5 + 7+7+ 1 + 1 =...
* SUBSET-SUM-kS, t> I S -[xi Xk] and for some lyı yn)cIxi.... xk) the sum of the yi's equals t. For example, <S-2, 3, 5, 7, 11, 14], t-21> is in SUBSET-SUM because 3+7 11-21. xk) can be partitioned into two parts A and -A where -A * SET-PARTITION <S> S-Ixi S-A and the sum of the elements in A is equal to the sum of the elements in A. For example, 〈 S-12, 3, 4, 7, 8/> works because...
PROBLEM 3. Prove or disprove the following: /V2V54 log2 (J18 V ) is an irrational number. PROBLEM 4. Find the number of different symmetric relations that can be defined on a set 1 - {a,b). PROBLEM 5. Let A - {2, 3, 4, 8, 9, 12), and let the relation Ron A be defined by aRb if and only if (abia#b). Find R.
We know that we can reduce the base of an exponent modulo m: a(a mod m)k (mod m). But the same is not true of the exponent itself! That is, we cannot write aa mod m (mod m). This is easily seen to be false in general. Consider, for instance, that 210 mod 3 1 but 210 mod 3 mod 3 21 mod 3-2. The correct law for the exponent is more subtle. We will prove it in steps (a)...
how to do these five problems how to do these 6 problems 4- Zeis a multiple } 1) Let Boteze is a multiple of 4 a) Prove that ASB b) Is BCA? Prove or disprove. 2) Let 4-CZ-3 scade Prove that A is equal to the set of even numbers. - PC-+7,rcz} 3) Let - EZ-4+3, rez} a) List 5 elements of A and 5 elements of B b) Is AC ? Prove or disprove. c) Is BC? Prove or...
3. (8 marks) Let be the set of integers that are not divisible by 3. Prove that is a countable set by finding a bijection between the set and the set of integers , which we know is countable from class. (You need to prove that your function is a bijection.) We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
both questions -3 4 7. Prove or disprove, A: R3 R3 is bijective (1-1 and onto), where the standard matrix for A is A = -2 1 -1 3 8. Let A: R2 R2 be the linear transformation that that stretches the a-axis by a factor of 3, and the y-axis by a factor of 4. Find the standard matrix for A. 127
Please answer question 3 Find all (infinitely many) solutions of the system of congruence's: Use Fermata little theorem to find 8^223 mod 11. (You are not allowed to use modular exponentiation.) Show that if p f a, then a^y-2 is an inverse of a modulo p. Use this observation to compute an inverse 2 modulo 7. What is the decryption function for an affine cipher if the encryption function is 13x + 17 (mod 26)? Encode and then decode the...
8. Let p be an odd prime. In this exercise, we prove a famous result that characterizes precisely when -1 has a sqare root 1 mod 4. (You will need Wilson's Theorem for one (mod p). Prove: a 2--1 mod p has a solution if and only if p dircction of the proof.) 8. Let p be an odd prime. In this exercise, we prove a famous result that characterizes precisely when -1 has a sqare root 1 mod 4....