Problem $3$

a$)$ The following function is a t$-$norm:

$TT(a,b)=\{\begin{array}{ccc}\text{m}\text{i}\text{n}& (a,b)if\text{m}\text{a}\text{x}(a,& b)=1\\ 0& \text{o}\text{t}\text{h}\text{e}\text{r}\text{w}\text{i}\text{s}\text{e}& \end{array}$

Specify the t$-$conorm associated with this t$-$norm $($in a form as simple as possible$).$

b$)A$ is a fuzzy subset of $Z$ such that ${}_A(0)=1,{}_A(1)=\frac{1}{2},$ and ${}_A(z)=0$ otherwise. Likewise, $B$ is a fuzzy subset of $Z$ such that ${}_B(5)=\frac{3}{4},{}_B(6)=1,$ and ${}_B(z)=0$ otherwise. Apply the extension principle to compute the sum of A and $B.$