Digital Electronics - Boolean Algebra and Logic Simplification - Discussion

By using Demorgans theorem (x+y)'=x'.y' is AND GATE.
(x'.y')=(x+y)' is NOR GATE.

So, option C is correct.

Please explain the answer.

OR gate have complement then produce the NOR gate and AND gate separated by dot (.).

Since the LHS of the expression is the logical expression of two inputs NOR Gate and the RHS of the expression consists of two inverted inpuuts of A and B, that is two inverted input are ANDed to get the RHS of the expression and since according to Demorgan Laws, the complement of the sum of two or more variables are equivalent to the product of the complement of the individual variables, we can say that a NOR gate is equivalent to an AND gate with inverted inputs.

Left side of the equation is the output of a two input nor gate (which simply inverts the output of an or gate) and right side of the equation is the output of an and gate with the inverted inputs (output of the and gate is the product of the given inputs).