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"Trade A for B"
"Trade A in exchange for B"
"Exchange A for B"

Do they mean the same thing " I give A so that I can get B" ?
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"Exchange A for B"
Do they mean the same thing " I give A so that I can get B" ?
I think so. See the examples here:

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exchange

1 a
: to part with, give, or transfer in consideration of something received as an equivalent <the boy exchanged his mother's cow for a handful of beans> b : to supply (something else) in place of goods returned <do you think the store will exchange something more up-to-date for the high shoes my aunt bought?>; also : to have (goods returned to the seller) replaced by other merchandise <I'm sure you can exchange the blouse but probably not return it for a refund>

2 : to part with for a substitute <exchanging future security for immediate enjoyment> : to lay aside, quit, or resign (something presently possessed) in return for some alternate <exchanged his youth and health for the burdens of wealth> <who would not exchange loneliness for happy companionship?>


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trade

EXCHANGE <reluctant to trade the security and rewards of private life for the hazards ... and the low pay of government office -- Time> <trade off the right to navigate the lower Mississippi for a slice of the Newfoundland fisheries -- E.S.Corwin> <trade a proven pitcher to another team for four rookies>


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Yes. Or, you could be the person who gave B to get A.

Your second example is a little redudant. You trade or you exchange.

"Trade" has a sense of things being equal. If you return something that isn't working to the store where you bought it and get a new part that does work, you exchange it.