Let f [a, b] → R be a bounded function. Then the followings are equivalent. (a) f [a, b] → R is Riemann integrable. : (b) For any & > 0, there exists a partition P of [a, b] such that U(f, P) L(f, P) < e. -

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

A:

Q: How to prove that a formula A is valid iff ¬A is unsatisfiable?

A:

Q: Prove that RQ is uncountable.

A:

Q: Prove the following by proof by contradiction: At least one of the 5 real numbers a, b, c, d, e is…

A: We will use basic properties  of inequality to proof this result by contradiction

Q: . Let a, b € Z so that 4a + 5b is a multiple of 13. Prove that 13 divides 9a + 8b.

A: We have to show that 13 divides 9a+8b To prove this we using 4a+5b divisible by 13

Q: = [a b] and B =[2³]. a. Compute AB. b. If AB = 1-5₂ 1. Let A = find the entries of A, i.e. find the…

A:

Q: Prove R is irreflexive iff R ∩ idA = ∅. If idA={ ∈ A x A |a=b}

A: In the given question we have to prove that a relation R defined on a set A is said to be…

Q: If A and B are independent, and the P(A) = 0.35 and P(B) = 0.45 find: a) P(A ∩ B)…

A: Given that P(A) = 0.35 P(B) = 0.45 A, B are independent events.

Q: Let a, b e R. Prove that if 15a + 206 = 49, then a and b are not both integers.

A:

Q: y = - 1.5 cos (3x -90) +0.5   what is the    a) period  b) amplitude  c) the phase shift

A: Since you have uploaded multiple part questions according to our guidelines we have solved the first…

Q: Disprove by Contradiction If a,b,c ∈ ℕ, then at least one of a-b, a+c and b-c is even.

A:

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

A:

Q: A counterexample can be used to prove a theorem is false. O True O False

A: We have to check

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

A: Given,A and B are independent events , so P(A∩B)=P(A)×P(B) .

Q: Ema thinks that (u) xw, exists. Paul disagrees with her. Who is right? Explain why.

A: Dot product gives a scalar value  .

Q: Suppose that a is a positive real number not equal to 1, and that r and s are positive real numbers.…

A: To prove that; rlogαs=slogαr  We have to show that the left hand side of the equation equal to the…

Q: Determine whether the following statements are True or False: A) For all positive integers a,b,…

A: using :- if a|b then a=bq , where q is unique integer.

Q: Find the greatest common divisor for 102 and 66, (102, 66), and the values of m and n such that…

A: To find the greatest common divisor of 102 &amp; 66. For that we can use Euclidian Algorithm.…

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: 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: (b) Let A and Bị be independent; similarly, let A and B2 be independent. Show that in this case, A…

A:

Q: If then A-¹- = A = [1 0 0 07 3 1 0 0 24 1 0 8 55 1

A: The given matrix, A=1000310024108551 We have to find an inverse matrix of A.

Q: let a, b, and m be integer, prove that if 2a+3b>=12m+1, than a>=3m+1, or b>=2m+1

A: To prove: For integer a, b, and m if   2a+3b≥12m+1Than, either a≥3m+1, or b≥2m+1.

Q: If P (B) = 1/4, P (A ∪ B) = 1/2 and P (A|B) = 2/3, then which of the following statements is true?…

A: GivenP(B)=14P(A∪B)=12P(A|B)=23

Q: why do we assume a|b and prove that way instead of ac|bc and prove back to a|b

A: why do we assume a|b and prove that way instead of ac|bc and prove back to a|b .

Q: Valero's 5k Fun Run was held yesterday in the downtown district. The top runner 4 runners (one of…

A: Given 1. Ralph finished 1 minute after the competitor in the white shirt. 2. The competitor in the…

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

A:

Q: . Consider the statement: Let A, B ∈ Z. If 6|A and 10|B, then 4|(A2 + B2). (a) Prove the statement.…

A: 5. Consider the statement: Let A, B ∈ Z. If 6|A and 10|B, then 4|(A^2 + B^2). (a) Prove the…

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

A:

Q: true. Show that (a v bc)(a Abc); but the converse is not

A: Solution: