What is the main purpose of the final step in the contradiction method?
Answer and explanation
Correct answer: To show that the initial assumption is false
A contradiction proof begins by assuming the negation of the statement to be proved. The reasoning then proceeds logically until it produces an impossible result or a conclusion that conflicts with a known fact or with an earlier condition. The purpose of the final step is to identify that conflict and reject the initial assumption. In the irrationality proof, assuming √2 or √3 is rational eventually forces the numerator and denominator to share a factor, even though they were chosen in lowest form. Therefore option A is correct. The final step does not create a new number, require a diagram, or replace reasoning with memorisation; it completes the logical disproof of the opposite assumption.
Frequently asked questions
What is the correct answer to this question?
To show that the initial assumption is false
Why is this the correct answer?
A contradiction proof begins by assuming the negation of the statement to be proved. The reasoning then proceeds logically until it produces an impossible result or a conclusion that conflicts with a known fact or with an earlier condition. The purpose of the final step is to identify that conflict and reject the initial assumption. In the irrationality proof, assuming √2 or √3 is rational eventually forces the numerator and denominator to share a factor, even though they were chosen in lowest form. Therefore option A is correct. The final step does not create a new number, require a diagram, or replace reasoning with memorisation; it completes the logical disproof of the opposite assumption.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Proof of irrationality of square root 2 and square root 3.
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