Each element in Z, except 0, has an inverse (Z,*) is commutative.

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: Prove that the multiplication is a binary operation on Q.

A:

Q: Suppose p = 5 and q RSA cryptosystem with public key (n, e) = (55, 7)? 11. Which of the following is…

A:

Q: Prove that RQ is uncountable.

A:

Q: Let is an operation defined on R by a*b=a+b-4, Va,beR. What is the identity element of the operation…

A:

Q: Define the binary operator # by: a#b = the smaller value of a or b.; Find each of the following: a.…

A: Here , a#b is defined as smaller value of a or b

Q: How do you derermine of RS → R* 76 onto?

A:

Q: Show that the number of binary operations on {1, 2} having 1 as identity and having 2 as the inverse…

A: Consider the given statement of the question,As we know that a binary operation * on A is a function…

Q: Determine the number of six-character passwords that can be formed using two letters from A to F and…

A: From A to F there are 6 letters. We can pick 2 letters from 6 letters in 6C2=15 waysIn 1 to 9 there…

Q: The notation aj + az + az + + an ak k=1 Σ is an example of notation.

A: The statement: The notation a1+a2+a3+...+an=∑k=1n ak is an example of ___________ notation.

Q: in the form af a +ib

A: Note that i=eiπ2 so, i=eiπ4.

Q: Р C = - = {₁²₁² +² -| 5 ≤ p ≤ 6 and − 1 ≤ q ≤ 1, p, q € N +1

A: Given: C=pq2+1 | 5≤p≤6 and -1≤q≤1, p,q∈ℕ we have to find the elements in the set C

Q: Suppose a is a real number. Suppose b additive inverses of a. and care Show that b = c. (Do not use…

A:

Q: Let A = { {a}, {b}, {c}, {d}, {e} } Determine by extension P(A

A:

Q: The_____ of A and B consists of all elements in either A or B or both.

A: The_____ of A and B consists of all elements in either A or B or both.   The answer of the above…

Q: Let * be a binary operation on R defined by a*b=a+b+2ab then find the identity element w.r.t. *. O…

A:

Q: 2. Find the following elements in Z₁9: a. 13 X19 17 b. 13 +19 17 c. -12 (the additive inverse of…

A:

Q: Let A = (a, b, c, d) and let # be a binary operation from A x AA presented by the following table: b…

A: Given that

Q: Let be a binary operation defined by a + b = 3ab find (a + b) * a Option 4 Option 3 9a²b 9ab Option…

A:

Q: Show all the work asap

A: Step 1: given matrix is: Let's say 'A' : A=⎣⎢⎡​10−1​43−3​110​⎦⎥⎤​, we have to find its inverse.The…

Q: Recall that each permutation can be written as a product of disjoint cycles. How many permutations…

A:

Q: 6. b. a. does not exist Find the inverse of -1 -1 Ed -4 نما 3 -4 -1 1 if it exists. C. 1 1 B 4 3 d.…

A: Given that the matrix 3-1-41

Q: Every permutations can be expressed as a   product of transpositions.

A:

Q: In the set {0,1,2,3,4,5}, this is the additive inverse of 4 under addition modulo 6. What is the…

A:

Q: Define a * b = ab – 3. Is a binary operation on z?

A:

Q: 1. List a pair of zero divisors of (M₂(Z), +, ×):

A:

Q: Let A = {small, medium, large}, B = {red, black}, and C = {pentagonal, round}. List the elements of…

A: Given : A =small, medium, largeB = red, blackC = pentagonal, round

Q: Define the binary operator  ⊗⊗ by:     a⊗b=a2+b+4a⊗b=a2+b+4  Find each of the following:…

A: The given question can be solved as shown in step2.

Q: Do the divisors of 24 form a Boolean algebra under gcd and lcm?

A:

Q: Let A be uncountable and B be countable. Prove that A\B is uncountable.

A:

Q: Each character in a password is either a digit [0-9] or lowercase letter [a - z]. How many valid…

A: We have to find how many valid passwords are there with the given restriction(s).

Q: Show that af +...+ a, = a1 + ...+ ap(mod p).

A: