, Let U = {n|n is a whole number and 2 sns 25), S = {nn E U and n is a square number), and p= {n n EU and n is a prime number} (n >1 is prime when it is divisible by just two different whole numbers: itself and 1). Let T = {nn EU and n is a power of 2}A %3D (a) Write S, P, and T in listed form. (b) Find the following sets: P, SNT, SUT, and SnT. 2. Draw a Venn diagram of the sets S, P, and T in problem 1. 3. Replace each box O with one of the symbols n, U, C, C, o = to give a correct statement for general sets A, B, and C. (a) A AUB (b) If A CB and A is not equal to B, then A B. (c) A (BU C) = (A N B) U (AN C) (d) AOØ = A

Q: Show that the permutations (12) and (12345) generate S5.

A: We have to show that the permutation 12 and 12345 generates S5. Suppose H=12,12345. We know that…

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…

Q: 5. Let 02(n) be the sum of the squares of the divisors of n 0₂(n) = Σd². din Make a guess at a…

A: It is given that ,    then

Q: Let U = {1, 2, 3, 4, 3, G, 7, 0, 9, to ; A = { positive even Factors OF to; {1,3,8,9} and {x Ix ic a…

A:

Q: 5. Let a = 2, az = 4, and an+2 a, = 2" for all natural number n. = 5a+1 - 6a, for all n 2 1. Use the…

A: Given information: The given values are a1=2,a2=4 and  an+2=5an+1-6an for all n≥1. To prove : an=2n…

Q: 5. If ged(a, n) = 1 then the order of a in (Z/nZ)× is the smallest integer i such that a¹ = 1( mod…

A: Since gcd(a, n) = 1, then             aφ(n) ≡ 1 (mod n)  Now, let order(a) = k.        => by…

Q: , Let a be a positive integer, where the positive difference of every two digits of a in base 10 are…

A: Here, For 1113,     | 1-1 | =0 , | 1-3 | = |-2| = 2 For 2000,     |2-0|= 2, |0-0|= 0 For 2022,…

Q: How many permutations π of [10] satisfy π^5 = 1?

A: The given set is 10=1,2,3,…,10. Therefore any permutation π of 10, is bijective function from the…

Q: If P(A)=0.2, P(B)=0.3 an d :P(ANB)=0.1, then P(A'UB) is

A: As per bartlby guidelines we can answer only first question and rest can be reposted  Given:…

Q: QUESTION 7. Find the number of permutations of length 9 that satisfy the following conditions: (i)…

A: To find- Find the number of permutations of length 9 that satisfy the following conditions: It…

Q: Let c, a, B be nonzero real numbers such that c + B. Find a given that 00 192n-3 ac? >18 %3D ch-4 с…

A: To find a from the given summation.

Q: 61 Let A = Compute 612 - A and (612)A. 4 2

A: Step 1: Step 2: Step 3: Step 4:

Q: 3n 3. Which of the following is the correct expansion of E-2(-1)" ()? c. (-;+"-#+) 243 243 + 6. 27…

A: The correct expression is option (D).

Q: Let o (n) be the sum of the divisors of n and let (n) be the Euler phi functions. Let n = = pq be…

A:

Q: k = 4 4. Let k be the second smallest nonzero digit of your Student ID. Compute the order of (k, k)…

A: To find the order of (4,4) .

Q: Find all 6 permutations of (12)(345).

A: Find all permutations with 12 in the first pair of bracket : (12)(345) (12)(354) (12)(435) (12)(453)…

Q: 6. 1. |A| = |-3 7 -1 2 -4|. Verify the expansion of A. a. About the third row b. About the first…

A:

Q: Prove ImA = A = Aln if A is m X n

A: Given: A be m*n matrix

Q: Use the method of Example 9.5.10 to answer the following questions. (a) How many 15-bit strings…

A:

Q: 4. Find the largest value of n such that 2"|16!.

A:

Q: If gcd(7, a) = 1, prove that either a +1 or a – 1 is divisible by 7. 20

A:

Q: (c) Suppose n EN is divisible by 5. What is (25n) (n) L?

A: Let, the prime factorization of n be as below.          n = p1a1 p2a2 . . . . . . pkak     for some…

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: Let A = 1 = {n+ (−1)n 2" | REN}. n Compute sup A and inf A if they exist.

A:

Q: 4. Convert (101001000)2 from binary to decimal notation and (1984)j10 from decimal to binary…

A:

Q: Please answer 4.1.15 A and 4.1.15B

A:

Q: Show that if p = q + 4a (p and q are odd primes), then (p/q) = (a/q).

A:

Q: Find d

A: The given question involves the concept of modular arithmetic and the use of the modular inverse.…

Q: p, q, pq | (apq − ap − aq  + a) for all a.

A:

Q: is a1 = 2, a2 =3, and an  = 5an–1 – 4an–2 for n > 2 expressed in explicit formula? true or false?

A:

Q: For which values of n does n! have n or fewer digits

A: Solution is as follows

Q: Let a = (17 3)(5 9 4 2) and B = (2 3)(7 4)(5 1 8) be elements of S10. Then, a'B is O (1 4)( 27 58 9…

A: Alpha square beta inverse is : (1 4)(2 7 5 8 3 9) Third option is correct.

Q: 6g 10 dno8ans 2. Let k be the second smallest nonzero digit of your Student ID. List the cosets of…

A: Please find the answer in next step

Q: 1 If the N(A) consists of all multiples of x = , then the rank of A 4 is: а. 3 O b. 2 O C. 4 O d. 1…

A: It is clear that from N(A)

Q: 12. Let the "Fibonacci-2" numbers g, be defined as follows: 91 = 2, 92 = 2, and gn+2 =( In+1)( In)…

A: