Αυτή σήμερα είναι λίγο κουρασμένη, αλλά είναι χαρούμενη.

to be

Breakdown of Αυτή σήμερα είναι λίγο κουρασμένη, αλλά είναι χαρούμενη.

• λίγο: a little
• σήμερα: today
• αλλά: but

Questions & Answers about Αυτή σήμερα είναι λίγο κουρασμένη, αλλά είναι χαρούμενη.

Why is the pronoun Αυτή used here? Could we leave it out?

In Greek, the subject pronoun (εγώ, εσύ, αυτός, αυτή, etc.) is often dropped, because the verb ending usually shows who is doing the action.

• Αυτή σήμερα είναι λίγο κουρασμένη... explicitly emphasizes “she”. It can sound like “She, today, is a bit tired…”, maybe contrasting her with someone else or with how she is usually.
• If you say Σήμερα είναι λίγο κουρασμένη, αλλά είναι χαρούμενη, it’s also correct and more neutral: “Today she is a bit tired, but (she) is happy.”

So yes, you can leave Αυτή out. Keeping it adds emphasis or contrast on “she”.

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Does Αυτή here mean “she” or “this (woman)” in English?

Αυτή can mean both “she” and “this (woman)”, depending on context.

• As a personal pronoun, it means “she”.
• As a demonstrative, it can mean “this one (feminine)”.

In this sentence, with no noun after it and in a simple context like “She is a bit tired today…”, it is most naturally understood as “she”.
If it were clearly demonstrative, you’d often see a noun:

• Αυτή η γυναίκα είναι κουρασμένη. – This woman is tired.

So here, read it as “she”.

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Why is the word order “Αυτή σήμερα είναι…” and not “Σήμερα είναι αυτή…” or “Σήμερα είναι λίγο κουρασμένη αυτή”?