$($d$)$ In the Unicode character system, there are characters for the fractions a half, a third and a quarter. Draw a deterministic finite state automaton over the alphabet $\backslash$Sigma $=\{(1)/(2),(1)/(3),\}$ that accepts only words that, when interpreted as sums of fractions, add up to $1.$ For example, your automaton should accept the words $(1)/(2)($as $+(1)/(2)+=1)$ and $(1)/(2)(1)/(2)($as $(1)/(2)+(1)/(2)=1),$ but not $(1)/(3)(1)/(2).$ You should aim to make your automaton minimal. That is$,$ it should use the smallest possible number of states.