Aa.16 H and K are subgroups

[karush]

Suppose H and K are subgroups of a group G. If $|H|=12$ and $|K|=5$, and $|H/K|$. Generalize.
$\vert H \cap K\vert=1$
then find $|H ∩ K|.Abstract Algebra
$H ∩ K ≤ H and H ∩ K ≤ K \implies |H ∩ K|||H| and |H ∩ %K|||K| \implies |H ∩ K||12 and |H ∩ K||35
\implies |H ∩ K|| gcd(12, 35)
\implies |H ∩ K|$

ok hopefully this is basically correct but what is the markup code for implies

https://dl.orangedox.com/XIYqaX59YzCfCQoBcb