Which of the following is a true statement?

Mathematics

1 answer:

mrs_skeptik [129]3 years ago

8 0

C is the correct answer

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Pigeon Hole Principle :

yaroslaw [1]

Answer:

A proof can be as follows:

Step-by-step explanation:

Let $S=\{a_{1},a_{2},...,a_{n},a_{n+1}\}$ be a set of $n+1$ integers. By the division algorithm the possible remainders when we divide by $n$ are $0,1,2,....,n-1$ . Then, each integer $a_{i}\in S$ can be written as:

$a_{i}=np_{i}+r_{i},\,\,0\leq r_{i}$

Observe that the set of remainders $\{r_{1},r_{2},...,r_{n+1}\}$ has $n+1$ elements and each element has $n$ possible values. By the Pigenhole principle at least two remainders have the same value. Suppose that this two elements are $a_{i}, a_{j}$ . Then,