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Specialist Mathematics · Unit 1 · Introduction to proof · The nature of proof

Use proof by contradiction.

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Question 1

Use proof by contradiction to determine which statement about the equation $x^2 + 5x + 3 = 0$ can be proven to be true.

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Question 2

A proof by contradiction is used to prove that quadrilateral ABCD is a parallelogram. Which of the following would be the correct assumption to start the proof?

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Question 3

Use proof by contradiction to show that if \(n^2\) is divisible by 5, then \(n\) is divisible by 5, where \(n\) is a positive integer.

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Question 4

Use proof by contradiction to show that if $n^2$ is an odd integer, then $n$ must be an odd integer.

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More in The nature of proof

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Use implication, converse, equivalence, negation, contrapositive.
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Use the quantifiers ‘for all’ (∀) and ‘there exists’ (∃).
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