Show that any language A is recognizable if and only if A

Q: Prove the following equivalence. Show each step of your proof.

A: Here r→s≡~r∨s Hence  ~r→s≡~~r∨s         ≡r∧~s Now suppose r is true: Then r∨r∧~s is true. Hence…

Q: Let A and B be sets. Use a proof by contradiction to show that An (B – A) = 0. your proof must be by…

A: Solution a: Let's assume that A∩(B-A)≠ϕ Let  x∈A∩(B-A)⇒x∈A and x∈(B-A)

Q: If R is an integer domain, show that it contains exactly two elements a that satisfy a? = a.

A: Given R is an integral domain. We have to show that it contains exactly two elements a that satisfy…

Q: (2) (a) Show using set identities that AUBU(AN BNT) = AUBUT (b) Prove by contradiction that if A C…

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Q: Let a, b, x, y ∈Zbe such that ax+by= 11. May we conclude that gcd(a, b) = 11?Why or why not? (Write…

A: Consider the given information:Let a,b,x,y∈ℤ be such that ax+ by=11.

Q: Prove the statement; a – c is a divisor of ab + cd=→a – c is a divisor of ad + bc.

A: We need to prove the statement; a – c is a divisor of ab + cd => a – c is a divisor of ad + bc.

Q: Let x and be real numbers. Prove that a2 = y? if and only if a = y or æ = -y.

A: Let                x2=y2⇒x2-y2=0⇒(x-y)(x+y)=0⇒x=y  or  x=-y So, x2=y2 only if x=y  or  x=-y.

Q: Prove that if gcd(a, b) = 1, then gcd(a + b, ab) = 1.

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Q: Prove: If a > 0, then (1/a) > 0.

A: It is given that a> 0.It is known that if ab > 0 then a > 0 or b > 0 or a< 0 or b…

Q: Use the pumping lemma to show that the language {www | w E e {a,b}*} is not regular.

A: Consider the provided question, We need to show that the language www|w∈a,b* is not regular by using…

Q: Let the operation on N defined by a*b=a-b, Va,beN. Then, find the property which satisfies by the…

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Q: H AJKL AGHI. Complete the congruence statement. KL = 2 KL

A: Given △JKL≅△GHI

Q: Jin Let G beagreupsuch that I6tefs thens

A: Answer

Q: 15. Let A and b Show that the cquation Ax b does nol have a solution for all possible b, and…

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Q: Let T, Sn, n = 1, 2, ... be sets. Prove the following distributive laws: Ü(Tn s.) = Tn (ÜSs, n=1 n=1

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Q: Find all (p, q, r) such that ((p + -4) evaluates to 1.

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Q: a) Prove that the set { 1} is an adequate set of connectives. b) As a result of a) above or…

A: Given: The statement form is ¬P→Q∧¬R

Q: PvQv R= (~P = Q)v (~P = R)

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Q: Let P be the set of all positive factors of 90, and let / denote the 'divides' relation. Then the…

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Q: Let V3 = {(a, b)|a, b E R} with the following operations: (a₁, a₂) + (b₁,b₂) = (a₁ + b₁, a₂ + b₂)…

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Q: Exercise 4.7 Consider n observations for which yi = a + bxi, b > 0), holds. Show that r = 1.

A: Given that there are n observations. yi=a+bxi

Q: Use set identities or different proof method to show that: (A U B) n (B U A°) = B

A: To prove A∪B∩B∪Ac=B If A and B both are empty sets φ, then there is nothing to prove. If A=φ, B≠φ,…

Q: a) Let A = {4, {$}, ($, [$}}} and B = {1,2}. How many equivalence relations on A?

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Q: Determine all values of c so that each given condition is satisfied.

A: Consider the given: u = 2c0 Find the magnitude: u=22+c2+02u=4+c2

Q: Give numericaL example to represent this rule: a -For any nonnegative mumber a, any integer k, and m…

A: Proceed as shown below

Q: Prove if a e G, o(a) =n, then a = reN GCD(n,r)'

A: Given below the detailed solution

Q: Let jEZ (a) Prove directly the statement : If 3j, then 3j²

A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…

Q: (a) Prove that A° is open, A° C A, and if U CA is open then UC A°. (b) Prove that A is open if and…

A: Since it is not mentioned which part answer we are supposed to do, so we are doing first part.…

Q: What property of congruence is illustrated in the following? If ∠X ≅ ∠Y and ∠Y ≅ ∠Z , then ∠X ≅ ∠Z .…

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Q: For nonempty sets A, B, and C, |A| <= |B| and |B| <= |C|, then |A| <= |C|.

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Q: t if n is a of by com

A: Given as, n is an integer 3n+2 is even

Q: Let a1, a2, a3, . .., an be real numbers. Prove that at least one of them is greater than the…

A: We prove it by contradiction.

Q: an be cauchy, prove why a subsequence of (an) must also be cauchy.

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Q: Which of the following are equivalence relations? If they are not, which of the axioms fails? a) For…

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Q: a. Let S= Z (the set of integers). Define t < s by s – t is non-negative. Prove or disprove that…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: 10. Using the Chinese Reminder Theorem, compute the value of x € Z+ which satisfies the following…

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Q: Let A1, A2, ... , An be any n sets, n 2 1. Show that (U-1 Ar) = U=1 Ar %3D

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Q: a Let A Show that A is nonsingular if and d only if ad – bc + 0.

A: Known fact: A matrix is said to be invertible (nonsingular) if its determinant is nonzero.

Q: Suppose A is open. Consider the following statements: (i) If finitely many points are removed from…

A: Given: A is open (i)If finitely many points are removed from A, then A is still open. (ii) If…

Q: Let a * b = 2ab be defined on Z*. 1. Is * Commutative? 2. Is * Associative? 3. What is the identity…

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Q: * is said to be commutative in A for all a,b ɛ A Select one: O a a*b b * a O b.a * b = b * a Oc a+b…

A: * is said to be commutative in A for all a, b in A, if, Option (b) a*b = b*a

Q: a. If A and B are independent, and A and B are independent, show that A and B are also independent.

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Q: If A is nonsingular then A' is nonsingular. Select one: O True False

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Q: Express the following in closed form: (1+k)? k=1

A: The standard formula for the sum of integers is given by the expression ∑i=1ni=n(n+1)2. The standard…

Q: Prove the following equivalence. Show each step of your proof. (p →q)^q → q

A: Given, p→q∧q⇔q To prove this by using truth table.

Q: In the Hilbert-Ackermann axiom system, prove each of the following statements. Do not use the CP…

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Q: Queshicn Every finit Subsef of (IRITu) is clascel H.W.

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Q: Let (a,b)=1 Show that (a+b, a-b)=1 or 2. When is this GCD 1? When is 2?

A: Proof:It is given that gcd(a,b) = 1. So ax + by = 1.Let gcd(a + b, a – b) = d, then d|( a + b) and…