Answer:
a. true b. true
Step-by-step explanation:
<em>(a) If r and s are rational numbers, then (r+s)/2 is rational. </em>
true
rational numbers can be expresed as fractions
let be r=a/b and s=c/d being a,b,c,d integer numbers
d.a=e is an integer number because it's the product of two integers
b.c=f is an integer number because it's the product of two integers
e+f=g is an integer number because it's the sum of two integers
b.d=h is an integer number because it's the product of two integers
2.h=i is an integer number because it's the product of two integers
g/i=j is an integer number because it's the quotient of two integers
then
<em>(b) For all real numbers a and b, if a < b then a < (a+b)/2 < b</em>
true
lets analyze 2a < (a+b)
then 2a < (a+b) is true
lets analyze (a+b) < 2b
then (a+b) < 2b is true