I'm stuck in a problem, need Help.
Associative property States that
(a + b ) + c = a + (b + c)
Which is true
but what if i change the position of the numbers
(a + c) + b = a + (c + b)
Does it hold true for the associative Law because the answer will still be same..
Stuck in this problem. Need your help with proofs.
Thanks in Advance.
Yep, it's true, even when you permute the symbols. Associativity means that $$(a + b) + c = a + (b + c)$$ for any $a, b, c$ in the appropriate set (real numbers perhaps?). It doesn't matter what I substitute in for these variables, this will always be true. Here are some true statements that follow from this: \begin{align*} (q + l) + v &= q + (l + v) \\ (1 + 3) + 5 &= 1 + (3 + 5) \\ (a + b) + (x + 1) &= a + (b + (x + 1)) \\ a^x + (b^y + c^z) &= (a^x + b^y) + c^z \\ a + (c + b) &= (a + c) + b \\ a + (a + a) &= (a + a) + a. \end{align*} Basically, you can substitute any expression you like in for $a, b, c$, so long as they evaluate to a real number, and you will get a true statement.