  Employing a quadratic transformation formula of Rahman and the method of
`creative microscoping' (introduced by the author and Zudilin in 2019), we
provide some new $q$-supercongruences for truncated basic hypergeometric
series. In particular, we confirm two recent conjectures of Liu and Wang. We
also propose some related conjectures on supercongruences and
$q$-supercongruences.
