$($Undergraduate student$)$

$(100$ points$)$ Define five car's speed fuzzy sets: Very Low, Low, Middle, High and Very High on the universe $[0,100]($miles$/$hour$).$ Please define five relevant continuous mathematical fuzzy membership functions for Very Low, Low, Middle, High and Very High, respectively. Please show results clearly and completely:

$(1)$ Fuzzy Intersection: Low $\frac{}{b}ar(High)=?$

$(2)$ Fuzzy Union: Very Low Very High $=?$

$(3)$ Fuzzy Complement: $\frac{?}{\text{b}\text{a}\text{r}}(High)=?$

$(4)$ Middle $\frac{}{b}ar(High)=?$

$(5)$ Very Low $\frac{}{b}ar(High)=?$

Break down the steps please