for any set X, construct and injection from X to Power set of X this is what i think, if i assume X to be {1,2,3}
then P(x) will have {{1},{1,2},{1,2,3},{1,3},{3,2},{3,2,1},etc}}
so will not, to say, 1 from X map to more than one element of P(x) ? so how can i prove for injection ?

For every $x \in X$, map $x$ to $\{x\} \in 2^X$. This is an injection.
