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In how many ways can a prime or an odd number be chosen from {1,2,3,4,5,6,7,8,9,10}?

Answer» We form two sets P and O as follows.
`P={2,3,5,7}` (primes) and O={1,3,5,7,9} (odd numbers).
On applying the general form of Sum Rule we get.
`n(PcupO)=n(P)+n(O)-n(PcapO)=4+5-3=6`.
We note that the numbers 3,5 and 7 are counted among primes and also among odd numbers.
So, we discount 3 (common numbers) from the sum `n(P)+n(O)`.


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