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Proof by Contradiction (Edexcel A-Level Mathematics): Quizzes

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Proof by Contradiction

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What is the first step in a proof by contradiction?

Assume the opposite of what you want to prove

What must you explicitly state when finding an inconsistency in a proof by contradiction?

'A contradiction'

What is the correct negation of 'all numbers are even'?

Not all numbers are even

To prove no greatest integer exists, after assuming greatest integer $k$ exists, what do we consider?

The integer $k + 1$

To prove if $n^2$ is odd then $n$ is odd, what do we assume at the start?

$n^2$ is odd and $n$ is even

In the proof that if $n^2$ is odd then $n$ is odd, letting $n = 2a$ , what form is $n^2$ ?

$2(2a^2)$ which is even

In proving if $n^3$ is even then $n$ is even, what form does $n^3$ simplify to when $n = 2m + 1$ ?

$2(4m^3 + 6m^2 + 3m) + 1$

A number is rational if it can be written as $\frac{a}{b}$ where $a$ and $b$ are integers with what property?

No common factors

To prove $\sqrt{2}$ is irrational, we start by assuming $\sqrt{2} = \frac{a}{b}$ with what property?

$a$ and $b$ have no common factors

In the $\sqrt{2}$ proof, from $2b^2 = a^2$ , why must $a$ be even?

Because $a^2$ is even

In the $\sqrt{2}$ proof, after showing both $a$ and $b$ are even, what is the contradiction?

They share a common factor of 2

What is the correct negation of 'all multiples of 2 are also multiples of 3'?

At least one multiple of 2 is not a multiple of 3

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Proof by Contradiction

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Proof by Contradiction

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Proof by Contradiction

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Proof by Contradiction

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Proof by Contradiction (Edexcel A-Level Mathematics): Quizzes

Practise the questions

What is the first step in a proof by contradiction?

What must you explicitly state when finding an inconsistency in a proof by contradiction?

What is the correct negation of 'all numbers are even'?

To prove no greatest integer exists, after assuming greatest integer kkk exists, what do we consider?

To prove if n2n^2n2 is odd then nnn is odd, what do we assume at the start?

In the proof that if n2n^2n2 is odd then nnn is odd, letting n=2an = 2an=2a, what form is n2n^2n2?

In proving if n3n^3n3 is even then nnn is even, what form does n3n^3n3 simplify to when n=2m+1n = 2m + 1n=2m+1?

A number is rational if it can be written as ab\frac{a}{b}ba​ where aaa and bbb are integers with what property?

To prove 2\sqrt{2}2​ is irrational, we start by assuming 2=ab\sqrt{2} = \frac{a}{b}2​=ba​ with what property?

In the 2\sqrt{2}2​ proof, from 2b2=a22b^2 = a^22b2=a2, why must aaa be even?

In the 2\sqrt{2}2​ proof, after showing both aaa and bbb are even, what is the contradiction?

What is the correct negation of 'all multiples of 2 are also multiples of 3'?

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Proof

Proof by Contradiction

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Proof

Proof by Contradiction

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Proof

Proof by Contradiction

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Proof

Proof by Contradiction

Join 100,000+ A-Level students studying Quizzes with us.

To prove no greatest integer exists, after assuming greatest integer $k$ exists, what do we consider?

To prove if $n^2$ is odd then $n$ is odd, what do we assume at the start?

In the proof that if $n^2$ is odd then $n$ is odd, letting $n = 2a$ , what form is $n^2$ ?

In proving if $n^3$ is even then $n$ is even, what form does $n^3$ simplify to when $n = 2m + 1$ ?

A number is rational if it can be written as $\frac{a}{b}$ where $a$ and $b$ are integers with what property?

To prove $\sqrt{2}$ is irrational, we start by assuming $\sqrt{2} = \frac{a}{b}$ with what property?

In the $\sqrt{2}$ proof, from $2b^2 = a^2$ , why must $a$ be even?

In the $\sqrt{2}$ proof, after showing both $a$ and $b$ are even, what is the contradiction?