Question

A=set of all the letters in the word "AUXILIUM" write. (a) set A in roaster form. (b) the cardinal number of set A​

Answer 1

Answer :

a). Å = { A , I , L , M , U , X }

b). n(Å) = 6

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 { } .

Solution :

Here ,

The given word is " AUXILIUM "

Clearly ,

The word " AUXILIUM " comprises of the letters A , I , L , M , U , X .

Thus ,

If Å = set of all the letters in the word " AUXILIUM " .

Then ,

The set Å in its roster form will be given as ;

Å = { A , I , L , M , U , X }

Clearly ,

The set Å contains 6 letters .

Thus ,

The cardinal number of the set Å will be given as ; n(Å) = 6 .