Question

Use the method of contrapositive proof to prove the following statements.
a- The product of any five consecutive integers is divisible by 120. (For example, the product of 3,4,5,6 and 7 is 2520, and 2520 = 120·21)

Answer 1

Given:

The product of any five consecutive integers is divisible by 120

To prove:

prove the given statement.

Solution:

Using contra positive value:

Let x y are the number.

Where x be a product of consecutive integers and y  is divisible by 120 . So, according to the situation, the statement is: $x\rightarrow y$

According to  Contra positive: $\` y \rightarrow \`x$

The above equation defines that, if product "x" is not divisible by 120, 5 integers will not be consecutive.

$\`y$ = it will not be divisible by 120

$\`x$ = the product of 5 integers which are not consecutive .

Let say integers are 3,4,5,6, and 7.

consecutive product $=3\times4\times5\times6\times7$

                                    $=2520$

Product = 2520 is divisible by 120

Hence we have proved our result