Question $3$: Puzzy Logic and Systems $[24$ marks$]($a$)$ Given the set X $=(1,2,3,4),$ A and B are defined as follows: $-$ pa$(2)-0\mathrm{.}75,$ na$(3)=0\mathrm{.}35,$ na$(4)=0\mathrm{.}18-$ue$($l$)=0\mathrm{.}25,$ mb$(3)=0\mathrm{.}10,$ up$(4)=0\mathrm{.}02$ Compute A$,$ A n B$,$ AU A$.[6]$ Consider the following fuzzy expert system: RULE$1$: IF temperature is warm, THEN the swimming pool is crowded. RULE$2$: IF temperature is cold, THEN the swimming pool is quiet. Decision is to be made on the attendance in a swimming pole based on the temperature. The membership function in the universe of discourse are given as

r$-2510$

if $1525$

HWarm$($z