12. Which of the following polynomials is reducible over Q а) 4x3 + x — 2 b) Зх3 — 6х? +х - 2 c) 5x3 + 9x2 – 3 d) None of the above

Q: Simplify the expression [(a'^b)v (av b')]v (a'nb^c) by using the laws of Boolean algebra.

A: By using laws of boolean algebra,    De Morgan's law  Double Negation Idempotent Law Absorption law…

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A: The given problem is to find the singular value decomposition for the given matrix. Given matrix is…

Q: Look at the following statement proof: Proof Statement 1. VA, B, CCU,C – (AUB) = (Aº – C) U (Bº − C)…

A: (a) Let us consider the following sets.              A = {1, 2}            B = {2, 3}            C =…

Q: how to find the value of U(n) on abstract algebra example U(8) = {1,3,5,7}

A: By the definition , U(n)={ a: a<n and gcd(a,n)=1}

Q: |3x+2l+1 = 6

A: Given, 3x+2+1=6

Q: prove that a ∩ (b - c)=( a ∩ b)-(a ∩ c)

A: To prove: A∩B-C=A∩B-A∩C First prove, A∩B-C⊆A∩B-A∩C as follows.

Q: Find the rank(A) and null(A). 1 -3 -1 9 . -6 -1 4 -2 -10 -3 9. -6 -6 -3 3 -9 4 9 a) 1; 4 b) 2; 3 c)…

A: Rank(A) and Nullity (A)

Q: Is the statement true or false? (Va, b, c E Z, (ab | c) (a | c) ^ (b | c)) → (Va, b, c E Z, (a | bc)…

A: False

Q: We expect a car's highway gas mileage to be related to its city gas mileage. Data for all 1198…

A:

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A:

Q: If f(x) =. x - 1, then f({-1,0, 1, 2}) =

A:

Q: ихw3 (4, 5, 8) w x v = (6, 2, 6) Then (u +2 v+ w)x w =

A: Given u×w=(4,5,8)=4i+5j+8kw×v=(6,2,6)=6i+2j+6k

Q: 6. There are real numbers a and b such that Tarb = √at VE Proof: Let

A:

Q: 4. Prove: A\ (BNC) = (A \ B) U (A \ C)

A: A\ B = A-B .

Q: QUESTION 3 Construct the Operation Table for U(15)

A: Cayley table

Q: With U={1,2,3,..,9,10} and A={1,2,3,4,5} B={1,2,4,8}, C={1,2,3,5,7}, D={2,4,6,8}. Determine C' u D'…

A: Let X be the universal set and A be a subset of X. Then the complement of the set A is denoted as A'…

Q: Given the graph of f () below, which of the following could represent the graph of f' (x)? (0, 4)…

A: Given query is to find the graph of f-1(x).

Q: topology advanced make proof , application with 2 example for baire theoream

A: Baire's Theorem:Baire's Theorem is a fundamental result in functional analysis and general topology.…

Q: oltain The feterminant f The matria 3. 2-3 /- -3 5

A:

Q: gcd(n+1, n) =

A: To Find gcd(n+1,n)=?

Q: Cartesian Product Let A = {a, c, e, f, g} %3D Let B = {a, b, e, g} %3D Find the cartesian product of…

A:

Q: Show that addition and multiplication are well-defined, that is, if a~ a' and b~ b', then a +b~ a'…

A: Given: Addition and multiplication ℤ/pℤ is defined as, ap+bp=a+bp and ap·bp=a·bp respectively. To…