IMPORTANT RULES OF VENN DIAGRAM
we can arrive at certain general relations between the cardinal numbers of set, which are known as cardinal properties of the set.
1) n(A) + n(B) = 5 + 5 = 10, n(A U B) = 8, n(A ∩ B) = 2
n (A U B) + n(A ∩ B) = n(A) + n(B)
or, n (A U B) = n(A) + n(B) - n(A ∩ B)
As we all know that, if A & B are disjoint sets, therefore for disjoint set n(A ∩ B) = 0
n (A U B) = n (A) + n (B)
2) n(A) = 5, n(A)’ = 3, n(U) = 8.
n (A) + n (A)’ = n (U)
3) n(A U B) = 8, n (B) = 5, n ( A – B ) = 3, therefore
n (A U B) = n (B) + n (A – B)
4) n(A ∩ B) = 2 , n(A) = 5, n( A – B ) = 3, therefore
n(A) = n(A ∩ B) + n( A – B )
or, n (A – B) = n (A) - n (A ∩ B)
5) n(A U B) = 8, n(A ∩ B) = 2, n (A – B) = 3, n ( B – A ) = 3
n (A – B) + n ( B – A ) = n(A U B) - n(A ∩ B)
or, n (A U B) = n (A – B) + n (B – A) + n (A ∩ B)