using venn diagram identity the distributive law for three empty sets a,b,c
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Answer:
Here we are going to see the proof of the following properties of sets operations and De morgan's laws by Venn diagram.
The following are the important properties of set operations.
(i) COMMUTATIVE PROPERTY
(a) A u B = B u A (Set union is commutative)
(b) A n B = B n A (Set intersection is commutative)
(ii) ASSOCIATIVE PROPERTY
(a) A u (B u C) = (A u B) u C
(Set union is associative)
(b) A n (B n C) = (A n B) n C
(Set intersection is associative)
(iii) DISTRIBUTIVE PROPERTY
(a) A n (B u C) = (A n B) u (A n C)
(Intersection distributes over union)
(a) A u (B n C) = (A u B) n (A u C)
(Union distributes over intersection)
De morgan's law for set difference :
For any three sets A, B and C, we have
(i) A \ (B u C) = (A \ B) n (A \ C)
(ii) A \ (B n C) = (A \ B) u (A \ C)
De morgan's law for set complementation :
Let U be the universal set containing sets A and B. Then