Which of the following statements is false regarding the effect of a change in interest rates on options prices $($assuming all other variables are held constant$)?$

a$.$ an increase in interest rates will make call options more valuable

b$.$ an increase in interest rates will be favorable to someone who is short a put

option

c$.$ an increase in interest rates will make call and put prices less valuable because of its effect on the present value of the underlying price

d$.$ a decrease in interest rates makes call options more valuable

e$.$ a decrease in interest rates makes put options more valuable

f$.$ a&e

g$.$ c & d