Question

A = {x:xis a prime, x < 20). Bfx:x e W, x <10), then
(A-B) intersection of (B-A)

Answer 1

Answer :

(A – B) ∩ (B – A) = ∅

Note :

★ Set : A well defined collection of distinct objects is called a set .

★ Method of representing a set :

a). Roster / Tabular / Listed form

b). Set Builder form

★ Roster form :

→ All elements are listed .

→ Elements are separated by commas .

→ Elements are enclosed within braces { } .

→ The order of writing elements doesn't matter .

→ The elements are not repeated

★ Set builder form :

→ The common properties of elements are written .

→ The elements is described using symbols like x , y , z (mostly x) .

→ Whole description of the elements are enclosed within braces { } .

★ 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 .

★ Difference of sets : The difference of two sets A and B in the order ( also called relative complement of B in A ) is the set of all those elements of A which are not the elements of B .

→ It is denoted by (A - B) .

Solution :

• Given : A = { x : x is a prime , x < 20 }

• To find : B = { x : x € W , x < 10 }

We have ,

• A = { x : x is a prime , x < 20 }

→ A = { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 }

Also ,

• B = { x : x € W , x < 10 }

→ B = { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 }

Now ,

→ A – B = { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 }

– { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 }

→ A – B = { 11 , 13 , 17 , 19 }

Also ,

→ B – A = { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 } – { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 }

→ B - A = { 0 , 1 , 4 , 6 , 8 , 9 , 10 }

Now ,

(A – B) ∩ (B – A)

= { 11 , 13 , 17 , 19 } ∩ { 0 , 1 , 4 , 6 , 8 , 9 , 10 }

= ∅

Hence ,

(A – B) ∩ (B – A) = ∅