2. exercise 18, 19 page 188. determine if the following statements are true. if a statement is true, give a proof from the definitions. if a statement is false, give a counterexample.

(a) if r and s are rational numbers, then (r+s)/2 is rational.
(b) for all real numbers a and b, if a < b then a < (a+b)/2 < b

a. true b. true

Step-by-step explanation:

(a) If r and s are rational numbers, then (r+s)/2 is rational.

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

(b) For all real numbers a and b, if a < b then a < (a+b)/2 < b

true

lets analyze 2a < (a+b)

then 2a < (a+b) is true

lets analyze (a+b) < 2b

then (a+b) < 2b is true

here the number -5 is all of the following except a rational number.

step-by-step explanation:

three-fourths of an hour

36÷48=0.75

0.75=