If n + 1 integers are chosen from the set (1, 2, 3,..., 2n). where n is a positive integer, must at least one of them be even? To answer this question, let S = (1, 2, 3, necessary ✓ ✓ for at least one of the 2n), where n is a positive integer, and note that in S there are exactly elements of 7 to be even. Thus, the answer to this question is Yes v x odd integers. Since n + 1 is greater than the number of odd integers in T, it is

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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If n + 1 integers are chosen from the set
{1, 2, 3,..., 2n},
where n is a positive integer, must at least one of them be even?
To answer this question, let S = {1, 2, 3,..., 2n}, where n is a positive integer, and note that in S there are exactly
for at least one of the elements of T to be even. Thus, the answer to this question is Yes
necessary
X
odd integers. Since n + 1 is greater than
the number of odd integers in T, it is
Transcribed Image Text:If n + 1 integers are chosen from the set {1, 2, 3,..., 2n}, where n is a positive integer, must at least one of them be even? To answer this question, let S = {1, 2, 3,..., 2n}, where n is a positive integer, and note that in S there are exactly for at least one of the elements of T to be even. Thus, the answer to this question is Yes necessary X odd integers. Since n + 1 is greater than the number of odd integers in T, it is
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