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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.

 May 19, 2018
 #1
avatar+971 
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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

 

winkwinkwink

 May 19, 2018
edited by GYanggg  May 19, 2018

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