Question

draw and prove demorgan's law

Answer 1

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

(i)  (A u B)'  =  A' n B'

(ii)  (A n B)'  =  A' u B'

Proof by Venn diagram
A \ (B n C)  =  (A \ B) u (A \ C)



From the above Venn diagrams (2) and (5), it is clear that 

A \ (B n C)  =  (A \ B) u (A \ C)

Hence, De morgan's law for set difference is verified.

Now, let us look at the Venn diagram proof of De morgan's law for complementation.   

(A n B)'  =  A' u B'