I
noun
1
BAD : I would prefer to study in America or British.
GOOD : I would prefer to study in America or Britain.
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The name of the country is Britain (or Great Britain ).
British is an adjective: 'British industry', 'British Airways'.
2
See THE 12 (↑ the )
II
adjective
1
BAD : I am learning English at British Council.
GOOD : I am learning English at the British Council.
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the British Council : 'Professor Sinclair's visit was organized by the British Council.'
2
BAD : I am a student in the British Council.
GOOD : I am a student at the British Council.
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See IN 5 (↑ in )