verb
1
BAD : He sat there all morning seeing the planes taking off.
GOOD : He sat there all morning watching the planes taking off.
BAD : The teacher told us to see what he was doing.
GOOD : The teacher told us to watch what he was doing.
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see = notice something with your eyes, especially without concentrating or paying attention: 'Did you see anyone go out?' 'Turn the light on if you can't see.'
watch = look at someone or something and pay careful attention, especially for a long time: 'She watched the man with interest as he made his way through the crowd.' 'After dinner we usually sit down and watch the news.'
2
BAD : I'm sending you the magazine so you can see by yourself how beautiful the country is.
GOOD : I'm sending you the magazine so you can see for yourself how beautiful the country is.
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see sth for yourself (NOT by ) = check that something is really true,correct, as described etc by seeing it with your own eyes: 'If you think I'm exaggerating, come and see for yourself.'