: (i) X U Y = { 1 , 2 , 3 , 5 } (ii) A U B = { a , b , c , e , i , o , u } (iii) AUB = { 1 , 2 , 3 , 4 , 5 , 6 , 9 , 12 , . . . } (iv) A U B = { 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } (v) A U B = { 1 , 2 , 3 }Note : ★ Set : A WELL defined collection of DISTINCT objects is called a set . ★ Union of two sets : The union of two sets A and B is the set of all those elements which are either in A or in B or in both .→ This set is denoted by A U B .★ Intersection of two sets : The intersection of two sets A and B is the set of all those elements which are in COMMON in both A and B .→ This set is denoted by A ∩ B .(i) Solution :Here , • X = { 1 , 3 , 5 } • Y = { 1 , 2 , 3 } Thus , → X U Y = { 1 , 3 , 5 } U { 1 , 2 , 3 } → X U Y = { 1 , 2 , 3 , 5 } (ii) Solution : Here , • A = { a , e , i , o , u } • B = { a , b , c } Thus , → A U B = { a , e , i , o , u } U { a , b , c } → A U B = { a , b , c , e , i , o , u } (iii) Solution : Here , • A = { x : x € N and x is a multiple of 3 } → A = { 3 , 6 , 9 , . . . } Also ,• B = { x : x € N and x < 6 } → B = { 1 , 2 , 3 , 4 , 5 } Thus , → AUB = {3 , 6 , 9 , 12 , . . .} U {1 , 2 , 3 , 4 , 5}→ AUB = { 1 , 2 , 3 , 4 , 5 , 6 , 9 , 12 , . . . } (iv) Solution :Here , • A = { x : x € N and 1 < x ≤ 6 } → A = { 2 , 3 , 4 , 5 , 6 } Also , • B = { x : x € N and 6 < x < 10 } → B = { 7 , 8 , 9 } Thus , → A U B = { 2 , 3 , 4 , 5 , 6 } U { 7 , 8 , 9 } → A U B = { 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } (v) Solution : Here , • A = { 1 , 2 , 3 } • B = ∅ Thus , → A U B = { 1 , 2 , 3 } U ∅→ A U B = { 1 , 2 , 3 }