Theorem: If $r$ and $s$ are rational numbers, then the product of $r$ and $s$ is a rational number. Which facts are assumed in a direct proof of the theorem?

a$.rs=\frac{a}{b},$ where a and $b$ are integers $a0.$

b$.rs=\frac{a}{b},$ where a and $b$ are integers $b0.$

c$.r=\frac{a}{b},$ and $s=\frac{c}{d},$ where $a,b,c,d$ are integers and $a0$ and $c0.$

d$.r=\frac{a}{b},$ and $s=\frac{c}{d},$ where $a,b,c,d$ are integers and $b0$ and $d0.$

A sequence is defined by the recurrence relation $f_n=n*f_{n-1}-f_{n-3}.$ How many initial values are required so that the sequence is well defined for all $n0?$

a$.0$

b$.1$

c$.2$

d$.3$

Which string of parentheses is not properly balanced?

a$.(()())()$

b$.(()()(())$

c$.(()()()())$

d$.()(()()())$

Select the set that is equal to:

$3,5,7,9,11,13$

a$.\{xinR$: