Abstract Algebra Answers

Consider the following sets together with binary operations. Are they user-friendly? Z with binary operation z1 . z2 = 2z1 - 4z2 Is the set closed under the operation? Is the operation commutative ? Is the operation associative ? Is there an identity? If there is an identity element then does every element have an inverse relative to the operation _ Consider R together with x . y = x/y. Ask the same questions as in last example.

Read answer

Answered!

Question #97174 from Aakash

Abstract Algebra

Prove or disprove that C~ R as fields.

Read answer

Answered!

Question #94721 from Daniel

Abstract Algebra

1. which of the following statement is true a. \\(\\sim (p\\vee q)=\\sim (p\\wedge \\sim q)\\) b. \\((p\\vee q)\\wedge (p\\vee r)=p\\vee (q\\wedge r)\\) c. \\((p\\wedge q)\\wedge (p\\vee r)=p\\vee (q\\wedge r)\\) d. \\((p\\wedge q)\\vee (p\\vee r)=p\\vee (q\\wedge r)\\) 2. ____ reads “the goods are standard if and only if the goods are expensive” a. \\(\\sim (\\sim p\\wedge \\sim q)\\) b. \\(\\sim \\sim q\\) c. \\(p\\leftrightarrow q\\) d. \\(\\sim p\\wedge q\\)

Read answer

Answered!

Question #94720 from Daniel

Abstract Algebra

1. \\((p\\wedge q)= (q\\wedge p)\\) and \\((p\\vee q) = (q\\vee p)\\) implies an _____ a. Idempotent Laws b. Associative laws c. Distributive Laws d. Commutative Laws 2. given that\\(A=\\begin{pmatrix}1 & 2 & 3\\\\ 4 & 5 & 6 \\end{pmatrix}\\)\nand \\[B=\\begin{pmatrix} 1 & 2\\\\ 3& 4\\\\ 5& 6 \\end{pmatrix}\\]\n. Find AB a. \\(\\begin{pmatrix} 0 & 12 & 17\\\\ 19 & 26 & 31\\\\ 29 & 40 & 51 \\end{pmatrix}\\) b. \\(\\begin{pmatrix} 5 & 12 & 15\\\\ 19 & 26 & 31\\\\ 29 & 40 & 51 \\end{pmatrix}\\) c. \\(\\begin{pmatrix} 0 & 12 & 17\\\\ 19 & 26 & 31\\\\ 20 & 40 & 45 \\end{pmatrix}\\) d. \\(\\begin{pmatrix} 0 & 12 & 17\\\\ 7 & 10 & 31\\\\ 20 & 40 & 45 \\end{pmatrix}\\)

Read answer

Answered!

Question #94719 from Daniel

Abstract Algebra

1. ____is equivalent to \\((p\\vee q)\\) a. \\(\\sim (\\sim p\\wedge \\sim q)\\) b. \\((\\sim \\sim q)\\) c. \\((p\\leftrightarrow q)\\) d. \\((\\sim p\\wedge q)\\) 2. \\((p\\vee q)\\vee r=p\\vee (q\\vee r)\\) and \\((p\\wedge q)\\wedge r = p\\wedge (q\\wedge r)\\) implies an ___ a. Distributive Laws b. Commutative Laws c. Associative laws d. Idempotent Laws

Read answer

Answered!

Question #94509 from Sarada prasan Mandal

Abstract Algebra

Let d ∈N , where d ≠1 and d is not divisible by the square of a prime. Prove that N:Z[square root of d] maps N union {0} : N(a+b sqr root d) = |a^2 -db^2| satisfies the following properties for x,y belongs to Z[sqr root d]. 1. N(x) = 0 if x=0. 2 N(xy) = N(x)N(y) 3. N(x) =1 if x is a unit 4. N(x) is prime if x is irreducible.

Read answer

Answered!

Question #93911 from Gboyega

Abstract Algebra

If p*q = p^2-q^2-2pq. Find the inverse of p under the operation.

Read answer

Answered!

Question #92042 from Ambika

Abstract Algebra

State and prove generalized commutative law in a commutative semigroup

Read answer

Answered!

Question #91473 from Sajid

Abstract Algebra

Q. Find the dimension of the subspace of R4 that is span of the vectors (█(1¦(-1)@0@1)), (█(2¦1@1@1)),(█(0¦0@0@0)),(█(1¦1@-2@-5)) Q. Choose the correct answer. Q. Let b and c are elements in a group G and e is identity element of G. If b5=c3=e,then inverse of bcb2 is a. b2cb b. b3c2b4 d. b2c2b4

Read answer

Answered!

Question #89033 from rahul

Abstract Algebra

Let N ∈d , where d ≠1 and d is not divisible by the square of a prime. Prove that N:Z[square root of d] maps N union {0} : N(a+b sqr root d) = |a^2 -db^2| satisfies the following properties for x,y belongs to Z[sqr root d]. 1. N(x) = 0 if x=0. 2 N(xy) = N(x)N(y) 3. N(x) =1 if x is a unit 4. N(x) is prime if x is irreducible.

Read answer

Answered!

Ask Your question

Search & Filtering