Let $Y(x)$ denote the statement $x$ is yellow, $R(x)$ denote the statement $x$ is red, and let $F(x,y)$ denote

the statement $x$ flies faster than $y,$ where the universe of discourse for $x$ and $y$ is the set of all birds.

Express the following statements using quantifiers, logical connectives, and the predicates $Y(x),R(x),$

and $F(x,y).$

$($a$)$ All birds are either red or yellow.

$($b$)$ Yellow birds fly faster than all red birds.

$($c$)$ There is a red bird that flies faster than all yellow birds.

$($d$)$ There is a red bird that flies faster than all yellow birds, and flies slower than all other red birds.