قبل از‌ | پیش از، بعد از | پس از
What are the differences between the first and second entries of each set? Is it a matter of formality?

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Hi
Yes it is the matter of formality and «قبل از» and  «بعد از» are more common in speaking.
Good luck :)

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سلام پاتریک عزیز.
بله تفاوت این کلمات فقط دراستایل و در رسمی و غیر و رسمی بودن هست.
و البته گاهی اوقات هم در همنشینی کلمات
وکلمه «پیش»معمولا با «از آنکه » و یا «از اینکه »میاد. و اکثر موارد کاربردش به معنی «جلوی»است..
I hope I've managed to clarify it well.
I'd be happy to help you with your Farsi in my class.

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Actually, if I may, with all due respect to fellow Farsi enthusiasts and instructors, I believe the main difference is not the degree of formality here, although one group does tend to be used more often in spoken Farsi than the other (قبل از- بعد از) regardless of formal or informal context.  So in fact:

قبل از/ بعد از >>>>> loanwords taken from Arabic and used in Farsi
پیش از/ پس از  >>>>> Farsi words (not borrowed)

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قبل از/ بعد از =====> informal
پیش از/ پس از  ====> formal

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