If A and B be two sets containing 3 and 6 distinct elements resp. What can be the minimum no. of elements in AUB ? Find also the max. no of elements in AUB .

Question

ganeshie8 · Answer

hint-
minimum no. of elements :  if the small set is a subset of large set
max no. of elements : if both sets are disjoint

anonymous · Answer

@ganeshie8 so how does this work ?

ganeshie8 · Answer

example :
A = {a, b, c} 
B = {a, b, c, d, e, f}

here A is subset of B

AUB  = B

its the minimum we can have right ?

anonymous · Answer

minimum ? .. am sorry i hav just startd with this chapter .
how come AUB = B ?

ganeshie8 · Answer

ok.. np :)

AUB means what  ?

ganeshie8 · Answer

its a set with all the elements in A or B right ?

anonymous · Answer

yes

ganeshie8 · Answer

so if you put all the elements on A or B, what you wil get ?

ganeshie8 · Answer

A = {a, b, c} 
B = {a, b, c, d, e, f}

AUB  = {a, b, c } U { a, b, c , d, e, f}

ganeshie8 · Answer

AUB  = {a, b, c, d, e, f}

this is same as B right ?

anonymous · Answer

yeah .. okay now i understand :)

ganeshie8 · Answer

glad to hear  :P

ganeshie8 · Answer

similarly, of both sets dont have any common elements, 
we get MAX elements in AUB
as it will contain UNIQUE elements from both the sets

ganeshie8 · Answer

*if

ganeshie8 · Answer

ex : 
A = {1, 2, 3} 
B = {a, b, c, d, e, f}

AUB  = {1, 2, 3 } U { a, b, c , d, e, f}

AUB   will have 6+3 = 9 elements. this is the maximum elements possible !

anonymous · Answer

okay !

anonymous · Answer

what about the minimum ?

ganeshie8 · Answer

minimum you will get when one set has a copy of elements from another set

ex :
A = {a, b, c} 
B = {a, b, c, d, e, f}

AUB  = {a, b, c } U { a, b, c , d, e, f}
 = { a, b, c, d, e, f}

here, AUB   has only 6 elements which are the same as no. of elements in B. this is the minimum elements you can have in AUB

ganeshie8 · Answer

it makes sense ? all elements in A are there in B also. so, AUB   = B

anonymous · Answer

okay .. understood . Now can you tell me the meaning of disjoint set ?

ganeshie8 · Answer

no new elements are being added to B by union operation. so you will have minimum elements..

ganeshie8 · Answer

there is no such thing as disjoint set.
its "disjoint sets"

anonymous · Answer

okay sorry !

ganeshie8 · Answer

disjoint sets means, two sets that dont have any COMMON elements

ganeshie8 · Answer

A = {a, b, c}
B = {x, y z}

here, A and B are disjoint sets

anonymous · Answer

okay .. wow yu teach relli well :D

ganeshie8 · Answer

A = {a, b, c}
B = {a, y z}

here A & B are not disjoint sets.. as they have a common element "a"

ganeshie8 · Answer

ohh ty :D

anonymous · Answer

okay