From a survey of 100 people we found that 62 drink pepsi, 36 drink coke and 30 drink both. How many drink only Coke? How many dr
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The base case is the claim that
which reduces to
which is true.
Assume that the inequality holds for <em>n</em> = <em>k </em>; that
We want to show if this is true, then the equality also holds for <em>n</em> = <em>k</em> + 1 ; that
By the induction hypothesis,
Now compare this to the upper bound we seek:
because
in turn because