## Discrete Mathematics with Applications 4th Edition

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