Suppose (A,∗) be an associative, unital, binary operation with inverses. Show that if|A|≤3,then in fact, (A,∗)...

Suppose (A,∗) be an associative, unital, binary operation with inverses. Show that if|A|≤3,then in fact, (A,∗) isalsocommutative, even though we didn’t assume it at the beginning.

Expert Solution

Colby Messinger answered 2 years ago

Suppose that a set G has a binary operation on it that has the following properties:...

Suppose that a set G has a binary operation on it that has the following properties: 1. The operation ◦ is associative, that is: for all a,b,c ∈ G, a◦(b◦c)=(a◦b)◦c 2. There is a right identity, e: For all a∈G a◦e=a 3. Every element has a right inverse: For all a∈G there is a^-1 such that a◦a^-1=e Prove that this operation makes G a group. You must show that the right inverse of each element is a left inverse and...

(§3.4 # 3) Use the previous problem to show that the average number of binary comparisons...

(§3.4 # 3) Use the previous problem to show that the average number of binary comparisons required to sort n items is at least O(n log2 n).

Convert 110.7510 to binary and hexadecimal . Show the answer in both binary and hexadecimal....

Convert 110.7510 to binary ______ and hexadecimal ______. Show the answer in both binary and hexadecimal. There are ____________ kilobytes in a megabyte. Convert -13210 to a 16-bit 2’s complement in binary ____________ and hexadecimal ______________.

For each of the following determine whether ∗ is a binary operation on R. If so,...

For each of the following determine whether ∗ is a binary operation on R. If so, determine whether or not ∗ is associative, commutative, has an identity element, and has inverse elements. (a) a ∗ b = (ab) / (a+b+1) (b) a ∗ b = a + b + k where k ∈ Z (c) a ln(b) on {x ∈ R | x > 0}

Suppose that people expect inflation to equal 3%, but in fact prices rise by 5%. Describe...

Suppose that people expect inflation to equal 3%, but in fact prices rise by 5%. Describe how this unexpected high inflation rate would help or hurt the following: a. the government; (3%) b. a homeowner with a fixed-rate mortgage; (3%) c. a union worker in the second year of a labour contract; and (3%) d. a college that has invested some of its endowment in government bonds. (3%)

4. Suppose that people expect inflation to equal 3 percent, but in fact, prices rise by...

4. Suppose that people expect inflation to equal 3 percent, but in fact, prices rise by 5 percent. Indicate whether this unexpected higher rate of inflation would help or hurt each of the following groups. a homeowner with a fixed-rate mortgage. a union worker with a fixed labour contract a company that has invested some of its endowment in government bonds which pays a fixed rate of return. 5. Indicate how each of the following events would affect the aggregate...

Show that AES decryption is, in fact, the inverse of AES encryption

(6) Define a binary operation ∗ on the set G = R^2 by (x, y) ∗...

(6) Define a binary operation ∗ on the set G = R^2 by (x, y) ∗ (x', y') = (x + x', y + y'e^x) (a) Show that (G, ∗) is a group. Specifically, prove that the associative law holds, find the identity e, and find the inverse of (x, y) ∈ G. (b) Show that the group G is not abelian. (c). Show that the set H= (x*x=e) is a subgroup of G.

Let G be a group with the binary operation of juxtaposition and identity e. Let H...

Let G be a group with the binary operation of juxtaposition and identity e. Let H be a subgroup of G. (a) (4 points) Prove that a binary relation on G defined by a ∼ b if and only if a−1b ∈ H, is an equivalence. (b) (3 points) For all a ∈ G, denote by [a] the equivalence class of a with respect to ∼ . Prove that [a] = {ah|h ∈ H}. We write [a] = aH and...

Find the solution of the following operation for binary numbers 11011.111- * 100101.01 using2'complement

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