Important Properties

(i) If  A and B are overlapping sets,

n(A\cup B)= n(A)+n(B)-n(A\cap B)

(ii) If  A and  B are disjoint sets,

 n(A\cup B)= n(A) +n (B)

(iii) n (\cup) = n(A) +n(B)-n (A\cap B)+n \left ( (A \cup B)^c\right )

(iv)  n(A \cup B ) = n(A-B)+n(B-A)+n(A \cap B)

(v)  n (A-B)= n(A\cup B)-n(B) and   n(A-B) = n (A) -n (A \cap B)

(vi)  n(A^c)= n(\cup)- n(A)


If  A , B and  C are any sets,

(i) n(A \cup B \cup C) = n(A) +n(B)+n(C)\\-n (A \cap B)-n (B\cap C)-n (A \cap C)+n(A\cap B \cap C)

(ii)  (A\cup B)-(A \cap B) = (A-B) \cup (B-A)

(iii)  n ( A \times B \times C) = n(A) \times n (B) \times n (C)

(iv)  n (A) = P, n (B) =q, The number of relation from  A \text { to } B =2^{pq}

(v)  A \times (B \cup C) = (A \times B) \cup (A \times C)

  A \times ( B \cap C) = (A \times B) \cap (A \times C)

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