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? Why?

Pigeonhole Principle

Step-by-step explanation:

From series {1,22n} ; we need to select 'n + 1' integers.

Even integers series from above series = {2,4,62(n-1), 2n}

Odd integers series from above series = {1,3,52(n-2), 2n-1}

So, we can choose only n odd integers from the series. Hence, if we choose n+1 integers, atleast one of them have to be even integer.

is there a question here?

step-by-step explanation: