(4) If two events A and B are in sample space S, then P(S | A) = P(S | B) = 1, P(A| S) = P(A) and P(B|S) = P(B)

Q: What are the right three digits of 3402? Hint. Use Euler's theorem. What is o(1000)?

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Q: Suppose x is a real number. Prove that if x 2, then there is a real number y such that x =…

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Q: (4) Prove in two different ways that if a is a positive r number, then (a + 1)" > a" + na"-1:

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Q: Show that both ℝ and ℝ2 may be covered by countably many open balls.

A: The answer provided below has been developed in a clear step by step manner.

Q: Show that Sn is solvable when n ≤ 4.

A: Given: Sn. We have to show that Sn is solvable when n≤4.

Q: Use proof by contradiction to prove that if x + y > 2, then x > 1or y > 1 (or both).

A: The method of contradiction is used to prove a statement or a set of statements. The inverse of the…

Q: - BJ -1]. prove prove A²-A-51 = 0 3 If A =

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Q: (4b) Is Tâ onto? How do we know?

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Q: prove that div A マ - Kr

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Q: 5. Let F= [3,2,1] and r= [2,1,–3]. Compute the following: %3D a) Proj „F. b) Orth rF = F – Proj „F.…

A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

Q: How many counterexamples are needed to prove that a statement is false?

A: Suppose P(x) be the statement.

Q: Prave that toc all numbers a and b, if (a,b)=d and az df, b=dq+ then df, 6=dg, then.

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Q: he error funct couibnpo 2ha : used in proba a) Show that

A: Given:-   erf(x)=2π∫0xe-t2 .dt

Q: If all entries of A and A -1 are integers, prove that <let A = 1 or -1. Hint: What is det A times…

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Q: Sy²el+2y®dy

A: Consider the indefinite integral ∫y2 e1+2y3 dy to evaluate the above indefinite integral, use the…

Q: Prove bey wnduc hiou that for n22.

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Q: find fix) and

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Q: 2017 J Q3 + V5 in the form a+bV5, where a and b are integers. Without using a calculator, express -2…

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Q: Let a, be such that asb. Prove that tx Eqt ax cbx

A: Concept: We have a,b∈Q means that a, and b belongs to the rational numbers and a<b means that a…

Q: beta

A: According to the question,        First,  define some of the terms for…

Q: The houses of a row are numbered consecutively from 1 to 49.show that there is a value of x such…

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Q: If a is transcedental over Q then a^2 is also transcedental over Q

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Q: Showthat S subring of RIKRZ+R3

A: For the solution of the problem follow the next step.

Q: For two real numbers x and y, if 2x + 3y > 7. Prove by contradiction: 18, then either x ≥ 3 or y ≥…

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Q: 1. Prove that fraction where m is z-4

A: Given: zn-1z-1 ⇒zn-1nz-1 ----(1) Let apply the limit in equation (1) limz→1zn-1nz-1 ----(2) Let n=pq…

Q: 1) D Prove that 224 O 210

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Q: (49-12)3/2 +6 - dt

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Q: Prove: If a is a positive even integer and b is an odd integer, then (a,b)=(a/2, b).

A: Let d be gcd of a and b. Now, b is odd so d cannot be even or is odd.  Now, since d is odd and…

Q: How would I prove this?

A: To prove: The statement