Some Important Properties and Important Laws

(i)  \phi^c =\bigcup

(ii)  \bigcup^c = \phi

(iii)  A-B = A \cap B^c , B-A = B \cap A^c

(iv) A \bigcup A^c = \bigcup , A \cap A^c = \phi

Important Laws:

If  A, B and  C be any sets, then

(i) Commutative Law:

A \cup B = B \cup A

A \cap B = B \cap A

(ii) Associative Law:

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

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

(iii) Distributive Law:

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

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

(iv) De-Morgan’s Law:

(A \cup B)^c = A^c \cap B^c

 (A \cap B)^c = A^c \cup B^c

(v) A-(B \cup C)= (A-B)\cap (A-C)

      A-(B\cap C)= (A-B)\cup (A-C)

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