Prove or disprove that if (A U B) C (An B), then A = B

Q: 1: Prove that (c a) * H = (c b) * H implies that a H = b H

A: Given an equation. We need to prove that : a*H = b*H where H is a subgroup of a group ( say G). Also…

Q: Let R= {(a, b) : a <b} Prove or disprove that R is transitive.

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Q: 4. Prove that it cannot be the case that x E AB and x EB\C. (Hint: prove via contradiction).

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Q: 3. Prove that (An B)² C A × B.

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Q: Prove that det(AB) = det(A) · det(B) for any A, Bϵ M2x2(F).

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Q: Is A – (B U C)= (A – B) N (A – C)? Prove it or disprove it.

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Q: Prove that if m*( A)= 0, then m* ( A UB) = m*( B).

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Q: Prove that A C B if and only if B C Ā.

A: A set X is said to be a subset of another set Y, if every element in set X is also an element in set…

Q: Prove that |ab|= |a | |b| for any numbers a and b.

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

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Q: Prove that if A2 = A, then I − 2A = (I − 2A)−1.

A: Let A2=A To prove :  I − 2A = (I − 2A)−1

Q: 2. Prove that if a, b e R, then (a) -(a + b) = (-a) +(-b), (c) 1/(-a) = –(1/a), (b) (-a)·(-b) = a ·…

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Q: Give a natural deduction proof of ¬(A V B) from hypothesis ¬A A¬B.

A: Please find the answer in next step

Q: 4. Let a,b,c € Z where c | (a+b). Prove that gcd(a,c) = gcd(b,c).

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Q: 4 Show that a + B = B +a for all a, BE C.

A: We can write alpha and Beta in general form of element of complex number.

Q: Prove that if A ⊂ C and A ⊆ B ⊆ C, then either A ⊂ B or B ⊂ C.

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Q: let R be for of King and acR.UThen a3-a Prove all that R is commutative

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Q: Prove that ∀a, b, k ∈ Z that ((4|k) ∧ (k = ab)) ⇒ (2|a ∨ 2|b)

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Q: Prove this: A≤B iff AnB=A

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Q: Prove logically that " C, + "C, + "C, + …· +"C, = 2".

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Q: V = \ + 855-t Prove that act) = 32

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Q: Prove that if a|b and b|c, then a|c.

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Q: 3. prove that: det (AB) = det (A) det (B) a - (; ), » - ( ) 2 -1 7 2 B = 2 в 3 %3D

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Q: Prove that |A U B| + |A n B| = |A| + |B|

A: Let A and B are two sets. A = number of elements in the set A. B = number of elements in the set B.…

Q: Prove that B \ A = B if and only if A ∩ B = ∅.

A: We will use definition  of sets for proving following question

Q: Prove or disprove Arg)- Arg(z,) - Arg(z,)

A: The polar form of the complex number, z=x+iy , can be written as z=rcosθ+isinθ , where, r=x2+y2 and…

Q: Prove that (S ⋂ T)c = Sc ⋃ Tc and  (S  ⋃ T)c = Sc ⋂ Tc .

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Q: 49. Prove that (a – b) × (a + b) = 2(a × b).

A: The following properties of vectors are used in proving the given identity. a×a=b×b=0a×b=-(b×a)

Q: Prove or disprove that if {a,} and {b,} are Cauchy and b,n # 0. Then An is Cauchy

A: If an and bn are Cauchy and bn≠0, then anbn is not Cauchy. Result used: If an and bn are Cauchy and…

Q: Prove that OfVg.dr = ] (Vfx Vg) · N ds.

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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: If gcd(a, c) = 1 and gcd(b, c) = 1, prove that gcd(ab, c) = 1.

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Q: 4. Prove or provide a counter example for the following: (AU B)nC = (AnC)U(BnC)

A: We need to prove that(A∪B)∩C=(A∩C)∪(B∩C)If we have to prove that(AUB)∩ C C C…

Q: 3. Show that A is positive if and only if A B B for some B.

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Q: 3. Evaluate ". a, Inutc b. In u C. Inx+c

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Q: 4. Prove that (a) A\B=A\(ANB) (b) A\(B\C) = (A\B)U(ANC) (A\B)\C=A\(BUC) (c)

A: To prove the given equality we shall use the following rules 1.   A \ B=A∩Bc 2. De Morgan's Law:…

Q: Prove or disprove the following: Vne Z, n³ + n²+1 is odd

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Q: Let a, b,c € R4. Prove that c+a a+b b+c c+b a +c b+a Al

A: a,b,c∈ℝ+ab+bc+ca≥c+ac+b+a+ba+c+b+cb+a

Q: Prove or disprove that if ECR" is open, then (E) (E) = E.

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Q: Prove/Disprove: (¬A → ¬B) ® (¬C ^ A) = ¬(A v ¬B) → ¬(B –→ C)

A: Any two propositions are said to be equivalent if the truth value in each row of the truth table is…

Q: 3. Prove or disprove: If a | (b + c), then either a |b or a | c. h of the follo

A: Since you have asked for question number 3 , we have solved it for you.

Q: prove that a(a+b)=c(c+d). a b d

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Q: How to solve this?

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Q: Prove that A + (B + C) = (A +B) + C P, A+B

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Q: Prove this: A=B iff A° U B = Ω =

A: Solution : First prove left to right, If A⊂B is true , All elements of A are inside B, Then Ac is…

Q: 4. Let a,b,c E Z where c| (a+b). Prove that gcd(a,c) = gcd(b,c).

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Q: 4. Prove: Let a, b e Z*. If a|b and bla, then a = b or a = -b.

A: If a/b and b/a then prove that a=b , a=-b.