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Consider the following statements: Statement I: For f(x) = |x−1| + |x−2| + |x−3| with 2 < x < 3, the function acts as the identity function. Statement II: A mapping f : A → A given by f(x) = x is an identity function.

1. Statement I is false, Statement II is true
2. Statement I is true, Statement II is true; and Statement II correctly explains Statement I
3. Statement I is true, Statement II is true; but Statement II does not correctly explain Statement I
4. Statement I is true, Statement II is false

Correct answer: Statement I is true, Statement II is true; but Statement II does not correctly explain Statement I

Solution

Statement I is true because within the interval (2, 3), the function simplifies to f(x) = x - 1 + x - 2 + 3 = x, which behaves like the identity function. Statement II is also true as it defines an identity function, but it does not explain the specific behavior of f(x) in the context of Statement I.

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