Let A/B = {w| wx ∈ A for some x ∈ B}. Show that if A...

Let A/B = {w| wx ∈ A for some x ∈ B}. Show that if A is context free and B is regular, then A/B is context free.

Use the pumping lemma to show that the following languages are not context free. a. {0n1n0n1n| n ≥ 0}

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Colby Messinger answered 6 days ago

Given two languages A and B, let A/B denote the language {w | w x ∈...

Given two languages A and B, let A/B denote the language {w | w x ∈ A for some x ∈ B}. Show that if A is a context-free language and B is a regular language, then A/B is a context-free language. hint (construct PDAs)

Proposition 8.59. Suppose that X, Y, W, Z, A, B are sets. Let f : X...

Proposition 8.59. Suppose that X, Y, W, Z, A, B are sets. Let f : X → Y , W ⊆ X, Z ⊆ X, A ⊆ Y , and B ⊆ Y . Then the following are true: prove the following ? (1) f(W ∩ Z) ⊆ f(W) ∩ f(Z). (2) f(W ∪ Z) = f(W) ∪ f(Z). (3) f−1(A ∩ B) ⊆ f−1(A) ∪ f−1(B) 4) f−1(A ∪ B) = f−1(A) ∪ f−1(B). (5) X−f−1(A)⊆f−1(Y −A). (6) W...

(2)Please determine : FIRST: (A) W’(X) ; THEN: (B) W’(0); W(X) IS DEFINED BELOW: W(X) =...

(2)Please determine : FIRST: (A) W’(X) ; THEN: (B) W’(0); W(X) IS DEFINED BELOW: W(X) = [ (10* (X^4) ) – 8 ] * { [ (30*X ) + 25 ] ^ (0.5) } HOWEVER, YOU MUST USE LOGARITHMIC DIFFERENTIATION, NOT THE PRODUCT RULE; IMPORTANT NOTE : YOU WI LL NOT BE GIVEN A N Y CREDIT FOR USE OF THE PRODUCT RULE, IN ORDER TO OBTAIN THE DERIVATIVE OF T(X) ! SERIOUSLY – YOU M U S T USE...

Let T: V →W be a linear transformation from V to W. a) show that if...

Let T: V →W be a linear transformation from V to W. a) show that if T is injective and S is a linearly independent set of vectors in V, then T（S） is linearly independent. b) Show that if T is surjective and S spans V,then T（S） spans W. Please do clear handwriting!

Let Vand W be vector spaces over F, and let B( V, W) be the set...

Let Vand W be vector spaces over F, and let B( V, W) be the set of all bilinear forms f: V x W ~ F. Show that B( V, W) is a subspace of the vector space of functions 31'( V x W). Prove that the dual space B( V, W)* satisfies the definition of tensor product, with respect to the bilinear mapping b: V x W -> B( V, W)* defined by b(v, w)(f) =f(v, w), f E...

(10pt) Let V and W be a vector space over R. Show that V × W...

(10pt) Let V and W be a vector space over R. Show that V × W together with (v0,w0)+(v1,w1)=(v0 +v1,w0 +w1) for v0,v1 ∈V, w0,w1 ∈W and λ·(v,w)=(λ·v,λ·w) for λ∈R, v∈V, w∈W is a vector space over R. (5pt)LetV beavectorspaceoverR,λ,μ∈R,andu,v∈V. Provethat (λ+μ)(u+v) = ((λu+λv)+μu)+μv. (In your proof, carefully refer which axioms of a vector space you use for every equality. Use brackets and refer to Axiom 2 if and when you change them.)

Let w,v1,...,vp ∈ Rn and suppose that w ∈ Span{v1,...,vp}. Show that Span{w,v1,...,vp} = Span{v1,...,vp}. Let...

Let w,v1,...,vp ∈ Rn and suppose that w ∈ Span{v1,...,vp}. Show that Span{w,v1,...,vp} = Span{v1,...,vp}. Let v1,...,vp,w1,...,wq ∈ Rm. Is the following statement True or False? “If {v1, . . . , vp} is linearly dependent then {v1,...,vp,w1,...,wq} is linearly dependent.” If you answer True, provide a complete proof; if you answer False, provide a counter-example. Linear Algebra. Please show both!

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Let A/B = {w| wx ∈ A for some x ∈ B}. Show that if A...

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