1.

State Demorgen’s laws. Prove anyone with truth table method.

Answer»

Demorgan’s first theorem states that (A + B)’ = A’ . B’ 

ie. the complement of sum of two variables equals product of their complements, 

The second theorem states that (A . B)’ = A’ + B’ 

ie. The complement of the product of two variables equals the sum of the complement of that variables. 

Proof: 

Truth table of first one is as follows:

ABA +B(A + B)’A’B’A’ . B’
0001111
0110100
1010010
1110000

From the truth table the columns of both (A + B)’ and A’ . B’ are identical. Hence proved.



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