#### Answer

a. $R_{1}=\{(0,1), (1,1)\}, R_{2}=\{(0,1)\}, R_{3}=\{(1,1)\}, R_{4}=\{\}$
b. $F=\{(0,1), (1,1)\}$
c. $\frac{1}{4}$

#### Work Step by Step

The set of relations from $\{0,1\}$ to $\{1\}$ is given by the set of subsets (also called the power set) of $\{0,1\}\times \{1\}$. $R_{1}$ is the only relation that also qualifies as a function, because it maps every $x$ value onto exactle one $y$ value.