Could someone please check my work

Q 4 Let EAji jeJE be an indexied family of sets and let B be a Set. Prove The following ( a) B U [NA] ] = n ( BUA ; ) jes XEB U NA; iff XEB or XENA; (definition of union ) jeJ jeJ iff XEB or XEA; VieJ Cdefinition for indexe intersection ) iff XEB UEA; VjeJ ( definition of union ) iff XEn ( BUA ; ) (definition ) for indexed jeJ intersection ) ( 6) B n [ UA; ]= U (BNA. ) jes JET XEBn UAj iff XEB and XE UA; (definition of intersection JET 213 JEJ & / iff XEB and XEA; JieJ (definition for indexed union ) iff XEB n Aj FieJ ( definition of intersection ) iff XE U ( BNA ; ) ( definition for JEJ indexed union )