Question

answer of these questions ​

Answer 1

Answer :

(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 }