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1.1 Proof by Contradiction

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Question 77
a.

A student claims that 7 is the largest value of mmm in the interval 6<m<76 < m < 76<m<7.

Explain the error in the student's statement.

[1]
bi.

A teacher states that there is no largest value of mmm in the interval 6<m<76 < m < 76<m<7 and provides the following proof by contradiction:

Step 1: Assume there is a largest number in the interval 6<m<76 < m < 76<m<7 and let this largest number be LLL.

Step 2: Let n=L+72n = \frac{L + 7}{2}n=2L+7​.

Step 3: L<n<7L < n < 7L<n<7, which is a contradiction.

Step 4: Therefore, there is no largest number in the interval 6<m<76 < m < 76<m<7.

Explain the contradiction stated in Step 3.

[1]
bii.

Using a similar method, prove that there is no smallest value of mmm in the interval 6<m<76 < m < 76<m<7.

[3]
Markscheme

1.1 Proof by Contradiction Questions

  1. A Level
  2. /Maths
  3. /1.1 Proof by Contradiction

107 exam-style questions on Edexcel A Level Maths 1.1 Proof by Contradiction. Each one has a worked solution and a mark scheme showing where the marks go.

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