1)
AUB
U = Union mean write in sequence which also
include repeat one time.
Let’s Example two set one is A and another
one is B:
A =
{1, 2, 5, 8} B
= { 1, 3, 5, 9 }
AUB = A Union B
Answer.
AUB = { 1, 2, 5, 8 } U { 1, 3, 5, 9}
AUB ={1, 2, 3, 5, 8, 9} Ans.
Note : which show the indicate of different
color actualy write one this indicate means.
2)
A П B
П = intersection
Means write dupilcte value two set one
time.
A =
{1, 2, 5, 8} B
= { 1, 3, 5, 9 }
A П B
AUB = A intersection B
Answer.
A
П B = { 1, 2, 5, 8 } U { 1, 3, 5, 9}
AUB ={ 1 , 5 } Ans.
Difference Between Two Set ( A – B)
(A – B)
( --) show
difference between two set
We have sample
difference number it like same.
Let’s example :
(A-B)
A
= {1, 2,
5, 8} B = {
1, 3, 5, 9 }
Answer.
A
- B = { 1,
2, 5, 8 } -
{ 1,
3, 5, 9}
AUB ={ 2 , 8 } Ans.
Write only A set remaining value.
3)
( A U B) П ( A U C)
A = {a, ,b c } B = { b, c, d, e } C= { c, d, e, f, h }
Taking Left Hand Side First
( A U B)
( A U B ) =
{ a, b, c } U { b, c, d, e}
(AUB) = { a,b, c, d, e}
Taking right side
(A U C)
(A U C) = { a,b, c} U { b, c, d, e}
(A U C) = {a,b,c, d , e}
( A U B) П ( A U C) Taking
( A U B) П ( A U C) = { a,b, c, d, e
} П {a,b,c, d , e}
( A U B) П ( A U C) = { a,b,
c, d, e } Ans.
Example
De Morgan’s Law
(AUB)’ = A’ПB’
( ‘ ) show Universal number
Let’s
U { 1, 2, 3, 4, 5, 6, 7 }, A= {
1, 3 5, 7} B = { 3,4, 5, 6}
Solutions:
i)
Here U = {
1, 2, 3, 4, 5 , 6 , 7 }, A = { 1, 3, 5 ,7} and B= {
3, 4, 5, 6 }
First Taking Right Hand Side
AUB = { 1, 3, 5, 7, }
U { 3, 4, 5, 6}
AUB = { 1,3,4,5,6,7 }
|
We find now,
(AUB)’ = U – (AUB)
U – (AUB) = ( 1, 2,
3, 4, 5, 6, 7 ) – ( 1, 3, 4, 5, 6, 7 )
(AUB)’
= {
2 } because difference both
set.
|
U – ( AUB) = { 2
} =>
Taking Left Hand Side :
A’ПB’ =
> U – A =>
U -B
U – A = { 2,4, 6 }
|
A’ =
> U – A = {
1, 2, 3, 4, 5, 6, 7 } – { 1, 3, 5, 7
} = >
U- B =
{ 1, 2, 7 }
|
B’ =
> U – B = { 1, 2, 3, 4, 5, 6, 7 } - { 3,
4, 5, 6 } =>
A’П B’ =
{ 2 } Ans.
|
A’ПB’
= { 2,4, 6 }
П { 1, 2, 7 } =
>
(AUB)’ = A’ПB’
Now you see that both value become same this
means that we verify De – Morgam Rule.
Berlitz is Pakistan #1 English Language Learning Institute for Kids, Teens, Children and Adults.
ReplyDeleteEnglish Language for kids and Teens
Special Summer Camp for kids and Teens in Karachi Islamabad and Lahore.
Learning with Fun activities for kids and teens.
Summer camp for kids and Teens
Click to visit Website