Given the two statements $(1)$ "The cash operating cycle is the amount of days between making a sale and collecting money from customers." and $(2)"$If management underestimates the allowance for non$-$collectible accounts, this will cause net income for the period to be overstated." Which of the following is true?

a$.(1)$ is false; $(2)$ is false

b$.(1)$ is true; $(2)$ is true

c$.(1)$ is false; $(2)$ is true

d$.(1)$ is true; $(2)$ is false