訳(わけ)がないThere is no way, There is no reason, It is impossible, Cannot be

わけがない and ようがない・ようもない are similar in that both express impossibility. わけがない rejects something as logically unthinkable, e.g. 彼がそんなことをするわけがない ('There's no way he'd do that'). ようがない emphasizes that there is no way or means to do something, e.g. 助けようがない ('There's no way to help').

そうもない and わけがない are similar in that both express the unlikelihood of an event. そうもない suggests low probability based on observation, e.g. 雨が降りそうもない ('It seems unlikely that it'll rain'), while わけがない is an emphatic denial based on the speaker's logical conclusion, e.g. 勝てるわけがない ('There's no way we can win').

These expressions are similar in that both emphatically express negation, but they differ in nuance. ことはない implies something never happens, or literally 'there are no cases of (A)', e.g. 二度と会うことはない ('I'll never talk to him again / a second time.'). In contrast, わけがない expresses strong denial or impossibility, e.g. 負けるわけがない ('There's no way I can lose.')

Both of these patterns with わけ express negation, but with different nuances. わけではない denies a possible interpretation or assumption, e.g. 'it's not the case that (A)', while わけがない is a stronger, categorical denial, meaning 'there's no way that (A)' or '(A) is impossible'.

はずがない and わけがない are similar in that they both express a strong denial of a possibility, similar to the English 'There's no way that (A)', but with slightly different nuances. はずがない gives the sense that the speaker is drawing a conclusion based on their own reasoning, often with a sense of surprise or disbelief. In contrast, わけがない expresses an even stronger denial, as if the impossibility is an obvious fact.