Chapter 1.4, Problem 24P

Use deductive reasoning to tell whether each statement is true or false. If it is false, give a counterexample.

For all real numbers x, y and $z,(x+y)+z=z+(x+y)$.

To determine

To find : Whether the statement is true or false.

Answer to Problem 24P

True

Explanation of Solution

Given statement: For all real numbers x,y and z, $\left(x+y\right)+z=z+\left(x+y\right)$

Justification:

Let x,y and z be any real numbers.

We know that set of real numbers is closed under addition, so x+y is also a real number.

Now , by commutative law of addition, we have

a+b=b+a , for every real number a and b.

Now x+y and z are real numbers, so we have

  $\left(x+y\right)+z=z+\left(x+y\right)$

Therefore, given statement is true.