Can I use in this sentence these both verbs keeping the same meaning:
She realises or she grasps her life was unhappy.
e. it needs an object. org/dictionary/english/grasp
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No, because when grasp is used in that sense, it works as a transitive verb; i.e. it needs an object.
It finally dawned on her that her life was unhappy.
She came to the unfortunate conclusion that her life was unhappy.
He finds the concept of happiness difficult to grasp because he grew up in abject poverty.