Я объяснил ему правило.

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Breakdown of Я объяснил ему правило.

• объяснить: to explain
• правило: the rule
• ему: him

Questions & Answers about Я объяснил ему правило.

What cases are used in Я объяснил ему правило?

• Я is nominative (subject).
• объяснил is the past-tense verb.
• ему́ is dative (indirect object: to whom?).
• пра́вило is accusative (direct object: what?). For inanimate nouns like правило, accusative = nominative in form.

Why is there no preposition for “to” (as in “to him”)?

Russian usually marks the indirect object with the dative case instead of a preposition. So “to him” is just ему́ (dative of он), not a prepositional phrase.

Is объяснил perfective or imperfective? What’s the difference from объяснял?

• объясни́л is perfective (from объясни́ть): a completed, single whole event.
• объясня́л is imperfective (from объясня́ть): ongoing, repeated, or backgrounded action. Examples:
• Я объясни́л ему́ пра́вило. I explained the rule to him (and finished).
• Я объясня́л ему́ пра́вило. I was explaining / used to explain the rule to him.

How would the sentence change if the speaker is a woman?