Prove that 3:8 is equivalent to 12:32

Q: Exercise 10. Show that if AC B, then ACB.

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Q: 4 prove that 170 is Riomonn

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Q: 1. Prove that 7(x – 1) 2.

A: Let, f(x)= ex-7x+7 ,for x≥2. Differentiating both sides with respect to x, f'(x)= ex-7≥0 . This…

Q: 15. Prove that for each natural number n, 5+ ...+ (4n-3)(4n+1) 4n+1'

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Q: (2) Prove that 21+ + for all 21, 22 € C.

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Q: {X = I (mod 3) 2X= 2 (mod 5)

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Q: 6. Prove that if gcd(a , b) = 1, then gcd(a + b, ab) = 1.

A: We need to prove that if gcda,b=1 then gcda+b,ab=1 Let us on the contrary assume that  gcda+b,ab=c…

Q: State and prove fatau's lemma.

A: statement of fatau's lemma :- Let fn be a sequence of non-negative measurable function . and fn→f…

Q: LI) Prove that (3

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Q: B) Prove that (O) = ) CE) n –k

A: We use the combination formula to simplify both sides

Q: Determine whether the statement, tan 45° / tan 15° = tan 3°, is true or false. If the statement is…

A: Consider the given statement: Here the objective is to check whether the given statement is true or…

Q: Prove that 9 u,+24 . if and only if 9u, Hint: Use identity (1) om page 288.

A: As per the hint we will use the identity of Fibonacci sequence and some modular arithmetic to prove…

Q: Given that 7,=21+)i and Za= FatYai Prove that

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Prove that in Q(/-5) we have (3,1+ 2v-5)(3, 1 – 2-5) = (3).

A: To show the equality, first we take an element of the product and show that it is in (3) and then we…

Q: Theorem 3: Ifconverges to l, ther any subsequence ofalso comverges to l.

A: We have given that sn converges to l. Let snk be any subsequence of sn. We need to prove that snk…

Q: Which congruence postulate or theorem can be

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Q: Show that 100 1 arctan(100) – arctan(2) + Σ 1 < arctan(100) – arctan(2) + 1+ 22 1+ 1002 1+ k2 k=2 WI

A: Note that the function f(x)=11+x2 is a monotone decreasing function, i.e., f(x1)&gt;f(x2) whenever…

Q: prove (1+ )" in <4 for all n21

A: In the given question we have to prove that  1+1nn&lt;4∀n≥1 . we can prove this by two methods one…

Q: prove the ITT₂TT, ITKITI"

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Q: 1. Prove that In(1 + 1) <I for r 20.

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Q: Prove NIn, +oo[= 0 ! n=1

A: To prove that ∩n=1∞[n,∞)=∅. Suppose that x∈∩n=1∞[n,∞). Then, x∈[1,∞), x∈[2,∞),.... That is, x≥n,…

Q: Prove that √1+i√3+√1-i√3 = √6

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Q: 14. Prove that AC B if and only if An BC= 0.

A: The objective is to prove the above question.

Q: Prove that if ACØ then A = (Ø.

A: To prove the given statement.

Q: Prove that 4.999...=5.000...=5

A: Proof:Let x = 4.999, then 10x = 49.99.

Q: Q2-Prove that

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Q: Prove that the nth Fibonacci number fn≤αn−1, where α is the golden ratio.

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Q: 6. Prove that ER, # 0.

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Q: Show that gcd(a,n)=1 if these exist m and k such that ma+nk = 1.

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Q: Prove VEN+, 5+ 3n ≥ 22n+1

A: Introduction: The idea of mathematical induction aids in the proof of mathematical conclusions and…

Q: Prove (1.2), (1.3), and (1.4). &#160;

A: (a) Let x∈A∪B So, ⇔x∈A or x∈B⇔x∈B or x∈A⇔x∈B∪A So, A∪B=B∪A

Q: II. Prove the following. 3. 7|23n – 1, Vn EN -

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Q: Supplemer 5) 90° Supplement of 90° = %3D B) State whether the given pairs are supples 1) 24°, 156°

A: We have to find the supplement of 90°  And state whether the Given pairs are supplement. 24° , 156°

Q: 15. Prove that for each natural number n, s+ (4n-3)(4n+1) 4n+1 ...

A: Given The given expression is 11·5+15·9+·  ·  ·+14n-34n+1=n4n+1

Q: (3) prove That () 3

A: We have to use z = x + iy.

Q: Prove that 3|(52n – 1) for all ne N.

A: We prove it by mathematical induction. 1st step We show that the statement is true for n = 1.…

Q: Use Fermat's theorem, show that if ged(a, 155) 1 then a1 = a (mod 15

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Q: If a,,a,, a3,., a, are in HP, Prove that a,a, +a,a; +...+ a,.1 a, = (n - 1)a,a,.

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Q: 2. Prove that Qn [2, 3] ~ N.

A: Two sets A and B have the same cardinality if there exists a bijection (onto , one-to-one…

Q: Prove that if a > 0, k > 1, and ak -1 is prime, then a = 2 and k is prime. %3D

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Q: Obtain the values of In(/3 – i).

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Q: Prove that 41 | 220 – 1.

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Q: 10. Use Euler's Theorem to show that 5P(16), '=1 (mod 16). Show your work or explain your reasoning…

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Q: 3. Let AC BCR. Prove ACB.

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Q: Let α, β, γ ∈ Z. Prove: If  α2 + β2 = γ2. then α or β is even.

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Q: 9. Use Euler's Theorem to show that 3P(26). =1 (mod 26). Show your work or explain your reasoning…

A: To show it by Euler's theorem :-

Q: 4. Prove by mathematical induction that = 2+1 1. 20+2¹+2²+...+2"

A: We have to find solutions

Q: If p,q,r are prime number but p is not equal to q, then what is gcd(p,q)? If p|rq, prove that p|r…

A: Given that p, q and r are prime numbers and p≠q.