Further $q$-supercongruences from a transformation of Rahman

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.