If A and B are independent, prove that B and the complement of A are independent.

Q: Show that if ac|bc, then a|b.Show that if a|b and b|a then a=±b.

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Q: 50000 00012. [8] 2 [+] 剧 的条目 72 = 2 元 dx 衙路2跨小嶝小鸡小 1000 1

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Q: (2c) Prove or disprove the following statement: “ A UBCANB for any A and B "

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Q: Let A and B be sets. Prove that A U B = An B if and only if A = B

A: First show if A∪B=A∩B then A=B, then show that if A=B then we have A∪B=A∩B.

Q: Construct a proof that ZEIF = ZGIH. н

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Q: Show that if A ⊂ B, then C – B ⊂ C – A.

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Q: = Let a, b, and d be positive integers. Prove that if (a, b) : divides a, then (d, b) = 1.

A: Definition of gcd (a, b) =1 is a and b does not have common prime divisor. Using this we can easily…

Q: Let 4; = {0, i} . Find U4, and N 4. i= 1 | A;. i= 1

A: Given :  Ai =  0 , i    To find :  The union ∪i=1∞ Ai    and the intersection  ∩i=1∞ Ai   .

Q: Is the following true or false? Z∩N=Z

A: Z is the set of all integers, i.e.  Z={ ..., -3, -2, -1, 0, 1, 2, 3, ...} And N is the set of all…

Q: Verify that v2+ V5 is algebraic over Q.

A: Algebraic number :- An algebraic number is a number that is a root of a non-zero polynomial in one…

Q: Are u sure its not 1

A: It is given that a=0 and b=1.

Q: Let a, b and c be integers. Prove that if a does not divide b and a|(b+c), then a does not divide c

A: Let a, b and c be integers.

Q: et a, b, c be positive real numbers. a² 6² c² a c

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Q: Can you find a,b,c, and d (if exists) such that AB = BA.

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Q: Show that if AB = I, then det(A) 0 and det(B) # 0.

A: Here given as AB=In find determinant both sides detAB=detIndetAB=1

Q: Let A:= {2} and B:= {2,3,5}. Give the Cartesian product of sets A and B, furthermore the power set P…

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Q: X and  Y are randam variables then XeY is a randam variables.

A: Here, The X and Y are two random variables  Then XeY are also random variables we have to show Here…

Q: If a1, az, az,.-ans. be the A.P. and S, = a-1m+1+a-1m+2+a-1n+3 +.--+ am %3D Prove that :…

A: In this question we have to proof S1, S2, S3,.... are in Arithmetic Progression.

Q: Exercise 3. Suppose that A and B are independent. Argue that A' and B' are also independent.

A: P(A⋂B)=P(A)P(B)  when A  and B are independent.

Q: Prove that if r>3 and y > 4, then ry > 11.

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Q: Show that A × B ≠ B × A, when A and B are nonempty, unless A = B

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Q: Let B be a subset of R¹. Which of the following statements are correct? O If B is a base, then |B| =…

A: Let V be a subspace of Rn for some n. A collection B = { v 1, v 2, …, v r } of vectors from V is…

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: If A ⊂ B, can A and B be independent under any circumstances? Explain

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Q: Let a and b be two positive real numbers. Let p > 1 and q> 1 be such that + = 1 (q is called the…

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Q: Suppose gcd(ab,c)=1. Prove that abc | d if, and only if ab | d and c | d.

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Q: Prove: Provided it exists, (A-1)¯ = A.

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: -1 -2 -3 -4- 1 2 Let A = 1 1-

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Q: 1. Solve the equations below. Show your work. a.) x2 – 14x + 45 = 0 b.) 3x2 – 2x - 5 = 0

A: As per our company guidelines we are supposed to answer only one question kindly post other question…

Q: Prove the following statement in three different ways, using a direct proof, a contrapositive proof…

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Q: Prove that X and Y are independent if and only if R = 0

A: To prove that if x and y are independent then correlation between them R =0