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  4. Let f: x, y, z → 1, 2, 3 be a one-one mapping such that only one of the following three statements is true and remaining two are false: f (x) ≠ 2, f (y) = 2, f (z) ≠ 1, then

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Q. Let $f : {x, y, z} \to {1, 2, 3}$ be a one-one mapping such that only one of the following three statements is true and remaining two are false : $f (x) \ne 2, f (y) = 2, f (z) \ne 1$, then

Relations and Functions - Part 2

Solution:

Let $f (x) \ne 2$ be true and $f (y) = 2, f (z) \ne 1$ are false
$\Rightarrow f (x) \ne 2, f (y) \ne 2, f (z) = 1$
$\Rightarrow f (x) = 3, f (y) = 3, f (z) = 1$ but then function is many one, similarly two other cases.