The set of points of continuity when

$\text{⨍ }\left(\mathrm{x}\right)=\left\{\begin{array}{l}1 \mathrm{if} \mathrm{x} \mathrm{is} \mathrm{rational}\\ -1 \mathrm{if} \mathrm{is} \mathrm{irrational}\end{array}\right.$

$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{ }\left\{\begin{array}{c}1\mathrm{ }\mathrm{if}\mathrm{ }\mathrm{x}\mathrm{ }\mathrm{is}\mathrm{ }\mathrm{rational}\\ -1\mathrm{ }\mathrm{if}\mathrm{ }\mathrm{x}\mathrm{ }\mathrm{is}\mathrm{ }\mathrm{irrational}\end{array}\right.$

Is discontinuous for all x

between two rational numbers there will be irrational numbers

$\Rightarrow$Set of points of continuity is $\varnothing$

Option (2) is correct