Consider the function f: R \to\{0,1\} such that f(x)={\\begin{array}{cc}1 & \\\\text{ if }\\ x \\\\text{ is rational }\\ \ 0 & \\\\text{ if }\\ x \\\\text{ is irrational }\\\\end{array}. Which one of the following is correct?

Correct Answer is : The function is many-one onto

UPSC NDA II 2010 Mathematics Paper

Question : 75 of 120

Marks: +1, -0

Consider the function f:R→{0,1} such that
f(x)={

1	‌ if ‌x‌ is rational ‌
0	‌ if ‌x‌ is irrational ‌

.
Which one of the following is correct?

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