Why is the initial assumption considered false in the contradiction method?
Answer and explanation
Correct answer: Because it leads to an impossible situation
The governing concept is proof by contradiction, also called reductio ad absurdum. To prove a statement such as the irrationality of a square root, we temporarily assume the opposite—for example, that the number is rational and can be written as a fraction in lowest terms. Algebraic reasoning then produces a result that conflicts with the original lowest-form or divisibility condition. Since a valid assumption cannot logically lead to an impossibility, the assumed opposite statement must be false. Therefore, option A is correct. Being small, containing a decimal, or lacking a diagram has no role in deciding whether the assumption is false.
Frequently asked questions
What is the correct answer to this question?
Because it leads to an impossible situation
Why is this the correct answer?
The governing concept is proof by contradiction, also called reductio ad absurdum. To prove a statement such as the irrationality of a square root, we temporarily assume the opposite—for example, that the number is rational and can be written as a fraction in lowest terms. Algebraic reasoning then produces a result that conflicts with the original lowest-form or divisibility condition. Since a valid assumption cannot logically lead to an impossibility, the assumed opposite statement must be false. Therefore, option A is correct. Being small, containing a decimal, or lacking a diagram has no role in deciding whether the assumption is false.
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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
