Let A = { a,b,c,d,e,f,g,g} Consider the following subset of A.

$A_1$ = [a,b,c,d] , $A_2$ = {a,c,e,g,g}

$A_3$ = {a,c,e,g} , $A_4$ = {b,d} , $A_5$ = {f,h}

Determine whether following is a partition of A or not.

Justify your answer.

**Solution:**

**1]** {$A_1, A_2$}

$A_1$ = { a,b,c,d} and $A_2$ = {a,c,e,g,h}

$A_1 V A_2$ = { a,b,c,d,e,g,h}

$\because$ f E A but f e A, V$A_2$ and $A_1 n A_2 \neq \phi $

$\therefore$ {$A_1, A_2$} is not a perfect partition of A.

**2]** { $A_3, A_4, A_5$ }

$A_3$ = {a,c,e,g}

$A_4$ = { b,d }

$A_5$ = { f, d }

$A_3 n A_4 N A_5 = \phi$

$\because$ All the elements of A is either present in $A_3$ OR $A_4$ OR $A_5$ and $A_3, A_4, A_5$ are mutually disjoint sets.

$\therefore$ { $A_3, A_4, A_5$ } are perfect partitions of A.