20. (a) For all real numbers a and b, |a + b| = |a| + |b|

(b) For all real numbers a and b, bac + bbc = ba + bc.

(c) If f(x) and g(x) are linear functions, then f (g(x)) is a linear function.

bigguy1989
May 19, 2018

#1**+1 **

If you want me to prove these statements, here is the proof:

(a) is not true, all we need to do is show an example that doesn't satisfy these claims to counter the statement.

We say a = -2 and b = 3

\(|(-2)+3|=1\), \(|-2|+|3|=5\)

\(1\ne5\), therefore (a) is not true.

(b)

We once again can plug in numbers.

a = 0 and b = 2

0 + 4c = 0 + 2c

4 is not equal to 2, so (b) is not true.

(c)

This is true

GYanggg
May 19, 2018