If \( \mathrm{A}= \) the set of letters in the word 'JAIPUR' and \(...

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If \( \mathrm{A}= \) the set of letters in the word 'JAIPUR' and \( \mathrm{B}= \) the set of letters in the word 'JODHPUR',
verify the following results:
\[
n(\mathrm{~A}-\mathrm{B})=n(\mathrm{~A})-n(\mathrm{~A} \cap \mathrm{B})=n(\mathrm{~A} \cup \mathrm{B})-n(\mathrm{~B}) \text {. }
\]
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