Question

can you please explain it also​

Answer 1

Answer :

Option 3rd : ( 2 , 4 , 5 , 1 )

Note :

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

★ Cardinal number / Cardinality : The number of elements/members/objects in a finite set is called cardinal no. / Cardinality .

→ Cardinal no. of a finite set A is denoted by n(A) .

★ 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 .

Solution :

Here ,

=> A = Set of natural numbers less than 6 and whose great common divisor with 6 is 1 .

=> A = { n : n < 6 , n € N , gcd(n,6) = 1 }

=> A = { 1 , 5 }

Clearly , n(A) = 2

Also ,

=> B = Set of divisors of 6

=> B = { n : n|6 , n € N }

=> B = { 1 , 2 , 3 , 6 }

Clearly , n(B) = 4

{ Note : a|b is read as a divides b OR a is divisor of b }

Now ,

The union set of A and B will be ;

=> A U B = { 1 , 5 } U { 1 , 2 , 3 , 6 }

=> A U B = { 1 , 2 , 3 , 5 , 6 }

Clearly , n(A U B) = 5

Also ,

The intersection set of A and B will be ;

=> A ∩ B = { 1 , 5 } ∩ { 1 , 2 , 3 , 6 }

=> A ∩ B = { 1 }

Clearly , n(A ∩ B) = 1

Hence ,

The cardinalities of A , B , (AUB) and (A∩B) are 2 , 4 , 5 and 1 respectively .