233 Answered Questions for the topic Proofs

10/08/20

Order 9 of the following sentences so that they form a proof by induction of the statement: 1^2+2^2+3^2+...+𝑛2=𝑛(𝑛+1)(2𝑛+1)/6 for all natural numbers n.
Order 9 of the following sentences so that they form a proof by induction of the statement:12+22+32+...+𝑛2=𝑛(𝑛+1)(2𝑛+1)/6 for all natural numbers n.Options We will proceed by induction to prove... more
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10/08/20

Order 8 of the following sentences so that they form a proof by induction of the statement: 2^𝑛>4𝑛 for 𝑛>4.
Order 8 of the following sentences so that they form a proof by induction of the statement: 2n>4n for 𝑛>4.Options: Base Case: n=5 Inductive Hypothesis: Assume 2k>4k LHS: 25=32, RHS:... more
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Proofs Mathematics

10/06/20

Prove that ∀n ∈ N, 2 n−1 ≤ n!
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Proofs

10/01/20

Solve the Proof
Given: m<ABC = 90
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Proofs

09/16/20

Algebraic proofs
Given: AE=BD;CD=CE prove:AC=BC
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09/02/20

Proofs in matrices

Given that A2 = I, prove that at least one of (A-I) and (A+I) is singular. I don't know how to do proofs but i'd like to see how to approach these kinds of questions thank you!
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Proofs Matrix

09/01/20

Proofs and matrices

If A is a n x n matrix. Show that A^2 = 0, then if i - A is nonsingular and (i-A)^-1 = i + A Thank you!
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Proofs Algebra

08/19/20

Show that when you multiply an even number by any other number, the answer is always even.

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Proofs Algebra

08/19/20

) Show that when you add five times a number to three times that same number, the answer is always even.

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08/10/20

Show that the solutions of the differential equation dy /dx = f (y) are monotonic functions.
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Proofs Math Geometry

06/29/20

Proving Vertical Angles Are Congruent
Given: Angle 2 and angle 4 are vertical anglesProve: angle 2 is congruent to angle 4Statement options: m angle 2+ m angle 3= 180 m angle 3+ m angle 4= 180 angle 2 and angle 3 are a linear... more
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05/20/20

Logs in equivalent forms including proof
Prove logxxy -2logxy = 1 - logxy 
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Proofs

05/13/20

Give an example of a subset B ⊆ A whose power set P(B) has cardinality 4.
Let A be the set of letters in your full name. Give an example of a subset B ⊆ A whose power set P(B) has cardinality 4.
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Proofs Math

05/13/20

Prove that if n ∈ N is odd then 2019n 2 − 2020n + 2021 is even.
Prove that if n ∈ N is odd then 2019n 2 − 2020n + 2021 is even.
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Proofs Math

05/13/20

Use mathematical induction to prove that 7 divides 36n − 22n for any n ∈ N.

Use mathematical induction to prove that 7 divides 36n − 22n for any n ∈ N.
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04/26/20

Proof by natural deduction
1. (~F v X) ↄ (P v T) 2. F ↄ P3. ~P /T
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04/17/20

P is any point in arc APB and C is the midpoint of arc ACB. If chord AB cuts chord CP at E, prove that triangle APC is similar to triangle EAC
Please write a two-column proof. Also, there should ONLY be one given (statement).
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04/17/20

If P is any point on side AB of triangle ABC and F, K, E are the midpoints of AP, PB, and PC, prove that triangle FKE is similar to triangle ABC
Please write a two-column proof. Also, there should ONLY be one given.
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04/17/20

ABC and DEF are two isosceles triangles on bases BC and EF respectively. If AB : BC = DE : EF (proportion), prove that the two triangles are similar.
Please write a two-column proof. Also, there should ONLY be one given.
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04/17/20

ABC and DEF are two isosceles triangles on bases BC and EF respectively. If AB : BC = DE : EF (proportion), prove that the two triangles are similar.
Please write a two-column proof. Also, there should be ONLY given.*If you could*, please choose some of these statements and use some of these reasons to prove the statements true. (Those below are... more
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04/17/20

If P is any point on side AB of triangle ABC and F, K, E are the midpoints of AP, PB, and PC, prove that triangle FKE is similar to triangle ABC
Please write a two-column proof. Also, there should be ONLY given.*If you could*, please choose some of these statements and use some of these reasons to prove the statements true. (Those below are... more
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04/03/20

How can i show and prove rigorously that for all integers, i can paint all these segments red?
Three counters, A, B, C are placed at the corners of an equilateral triangle of side n. The triangle is divided into triangles of side length 1. Initially all lines of the figure are painted blue.... more
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Proofs

03/28/20

Need help answering proof question about differentiating on an interval
I am unsure about how to approach this question about differentiability and would appreciate some help on how to prove this.Suppose that g is differentiable on an interval I. Show that for all n in... more
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03/12/20

Prove that the set {v + w, v + x, w − x} is always linearly dependent

Let v, w, x ∈ Rn be vectors. Prove that the set {v + w, v + x, w − x} is always linearly dependent (even if {v, w, x} is linearly independent).
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03/12/20

If the set {v, w, x} is linearly independent, so is {v+w, v+x, w+x}
Let v, w, x ∈ Rn be vectors. Prove that if the set of vectors {v, w, x} is linearly independent, then so is the set {v + w, v + x, w + x}.
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