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Под Москвой
Where do the people of these example sentences live exactly? What is the difference between these phrases? How near or far these people live from the Red Square? Most confusing is the first one.
Мой друг живёт под Москвой.
Я живу в Москве.
Он живёт в Подмосковье.
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в = in/into/inside.
"под" in this case is "very close to borders (almost zero distance)". Imagine big city as "hill" or "mount" and this "под" as "under" will become a little bit more logical. This is why "под" is never used in reverse ("big city под small city" is illegal).
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Под Москвой - in the suburbs (not in Moscow exactly, but somewhere within driving distance).
N.b. под боком - close to someone (мои дети живут под боком - в соседнем доме; продуктовый магазин находится под боком)