Past exam of the year 1 of the computer science course of the University of Oxford / 2003 / Calculus, probability, linear algebra, discrete mathematics, logic and proof, and models of computation / 9 / a / Solution

The assertion is true. Every single finite string $w=b_1\cdots b_k$ over $\{0,1\}$ is denoted by the regular expression $b_1\cdots b_k$. The empty string is denoted by $ϵ$. Hence if $F=\{w_1,\dots ,w_m\}$ is a finite formal language, the regular expressiondenotes precisely $F$, with each $w_j$ read as its concatenation of symbols. This uses the defining union and concatenation operations for regular expressions. For $F=\varnothing$, use the regular expression $\varnothing$. Therefore