what is difference between restrict and constrain in these sentence:
In those days women led very restricted/constrained lives
The cramped living conditions severely restricted/constrained the children’s freedom to play.
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Learner's dictionary says that they overlap between constrain and restrict. The differences are often overlooked:
Both can be used in the senses of holding something back by force or of limiting or restricting one's actions.
Restrain is used more in the sense of preventing an action:
Congress must restrain spending next year.
The man turned violent and it took four officers to restrain him.
I wanted more dessert, but I restrained myself.
Constrain is used more in the sense of placing limits, restrictions, or controls on an action:
The beauty of our sport is that there are hardly any rules to constrain you.
Industry regulations must not constrain innovation.
The police hope to impose order and constrain violence.
In actual usage, this distinction may not be very significant to the overall meaning of the context in which the words appear.
So it depends what you want to convey. However, GNgram shows that restricted is more used than constrained with the nouns lives and freedom.
As I do not have access to OED, I will quote this ELU post:
According to the Oxford dictionary: Restriction, constraint, restraint, or limitation? These are all things that limit what you can do. A restriction is a rule or law that is made by someone in authority. A constraint is something that exists rather than something that is made, although it may exist as a result of someone's decision. A restraint is also something that exists: it can exist outside yourself, as the result of someone else's decision; but it can also exist inside you, as a fear of what other people may think or as your own feeling about what is acceptable:moral/social/cultural restraints. A limitation is more general and can be a rule that someone makes or a fact or condition that exists.