True or false?
a!(b!c!) = (a!b!)c!
I think its true...?
Assuming that a! = a factorial, then I agree.
True.
To determine if the statement is true or false, we need to examine the equation and evaluate each side independently.
Let's break down the equation:
Left side: a!(b!c!)
Right side: (a!b!)c!
To understand the factorials in the equation, let's first define what a factorial is. The factorial of a non-negative integer is the product of all positive integers less than or equal to that number.
Now, let's evaluate each side of the equation:
For the left side, a!(b!c!), you start by calculating the factorials of b and c, and then multiply them together. Finally, you calculate the factorial of a and multiply it by the previous result.
For the right side, (a!b!)c!, you start by calculating the factorial of a and b, and then multiply them together. Finally, you calculate the factorial of c and multiply it by the previous result.
If both sides of the equation yield the same result, then the statement is true. Otherwise, it's false.
In this case, after evaluating both sides, we can simplify the equation as follows:
Left side: a!(b!c!) = a!(b!c!)
Right side: (a!b!)c! = a!(b!c!)
Since both sides are equal, the statement is true.
Therefore, the statement "a!(b!c!) = (a!b!)c!" is true.