Chapter 11.1, Problem 42PPSE

Solution

To find if the given statement is true or false.

The given statement is true.

Given information:

The statement is:

  $a!+b!=b!+a!$

Concept:

Factorial of a positive integer is constant.

For instance,

  $\begin{array}{l}1!=1\\ 2!=2\\ 3!=6\end{array}$

Calculation:

From the given statement, two factorials of constant numbers are added.

It is known that changing the sequence of addition does not alter the final result.

Therefore two factorials can be added in any sequence, the result shall be constant.

Conclusion:

Hence, the given statement is true.