Question

What are Demorgan’s Law? Explain the use of Demorgen’s law with example.

Answer 1

There are two Demorgan's law.
1). Sum of complements is equal to complement of product. 
͞A  + ͞B + ͞C =( A.B.C) whole bar
2). Product  of complement is equal to complement of sum.
͞A.͞B.͞C = (A+B+C) whole bar

Answer 2

 The complement of the union of two sets is the intersection of their complements and the complement of the intersection of two sets is the union of their complements.These are called De Morgan’s laws.

Examples on De Morgans law : 

1) Let U = {1, 2, 3, 4, 5, 6}, A = {2, 3} and B = {3, 4, 5}. 
Show that (A ∪B) ' = A ' ∩ B ' .

Solution : 
U = {1, 2, 3, 4, 5, 6} 

A = {2, 3}

B = {3, 4, 5} 

A ∪ B = {2, 3} ∪ {3, 4, 5} 

= {2, 3, 4, 5}

∴ (A ∪ B) ' = {1, 6}

Also A ' = {1, 4, 5, 6}

B ' = {1, 2, 6}

∴ A ' ∩ B ' = {1, 4, 5, 6} ∩ {1, 2, 6} 

= {1, 6}

Hence (A ∪ B) ' = A ' ∩ B '