Set question De Morgan's law

1. ONLINE CLASS OF MATHEMATICS FOR
VIII CLASS
TEACHER : SIR AHSAN
TOPIC : SET

2. APPLICATION OF SET
UNION:
Arrange all the elements in ascending
order. Symbol of union is (U).
INTERSECTION:
To take common. Symbol of
intersection is (⋂).
COMPLIMENT:
Subtract any set from universal set. The
recognition of compliment is ( ‘ ).

3. Definition of De Morgan's law: The
complement of the union of two sets is equal
to the intersection of their complements and
the complement of the intersection of two
sets is equal to the union of their
complements. These are called De Morgan's
laws.

4. De Morgan’s Laws:
(A ⋂ B)' = A' U B'
(A U B)' = A' ⋂ B'

5. If U = {1, 2, 3, 4, 5, 6, 7, 8}
A = {1, 3, 5, 7}
B = {2, 4, 6, 8}
Prove (A ⋂ B)' = A' U B'

6. Solution:
(A ⋂ B)' = A' U B'
Taking L.H.S
(A ⋂ B)'
First we find (A ⋂ B)
(A ⋂ B) = {1, 3, 5, 7} ⋂ {2, 4, 6, 8}
(A ⋂ B) = { }
Now,
U - (A ⋂ B) = {1, 2, 3, 4, 5, 6, 7, 8} – { }
U - (A ⋂ B) = {1, 2, 3, 4, 5, 6, 7, 8}

7. Taking R.H.S
A' U B'
First We find A'
A' = U – A = {1, 2, 3, 4, 5, 6, 7, 8} – {1, 3, 5, 7}
A' = U – A = {2, 4, 6, 8}

8. Than we find B'
B' = U – B = {1, 2, 3, 4, 5, 6, 7, 8} – {2, 4, 6, 8}
B' = U – B = {1, 3, 5, 7}
Now,
A' U B' = {2, 4, 6, 8} U {1, 3, 5, 7}
A' U B' ={1, 2, 3, 4, 5, 6, 7, 8}
L.H.S = R.H.S
Hence proved