Single Choice

Let $$f$$ be an injective function with domain $$\{x, y, z\}$$ and range $$\{1, 2, 3\}$$ such that exactly one of the following statements is correct and the remaining are false $$f(x) =1, f(y) \neq 1, f(z) \neq$$ 2. The value of $$f^{-1}(1)$$ is:

A$$x$$
B$$y$$
Correct Answer
C$$z$$
DNone

Solution

Let us assume the 3rd statement is correct. As f is injective then $$f(y) = 1$$ or $$f^{-1}(1)=y$$

Assuming 1st statement to be correct necessarily makes 2nd true while assuming the 2nd to be true doesn't give any necessary conclusion so our assumption is the only one possible.

SIMILAR QUESTIONS

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