How do you make equivalent logical ckt from venn diagram?

Answer 1

A Venn diagram contains three different types of regions...areas of non-intersection, areas of intersection, and the area which is neither. The areas of intersection are logically equivalent to the AND function. The areas that aren't inside any of the circles are logically equivalent to the NOT OR (NOR) function. The areas in a single circle only use a the NOT and AND functions.

For example, if you have a Venn diagram of the set {0-9} showing two circles A and B which have intersection elements {4,8}, and the elements of A={1,2,4,5,6,8}, the elements of B = {3,4,7,8}, and the elements {0,9} are outside of both circles:

A OR A = A = {1,2,4,5,6,8}

B OR B = B = {3,4,7,8}

A AND B = {4,8}

NOT (A OR B) = {0,9}

A NOT B = A AND (NOT B) = {1,2,5,6}

B NOT A = B AND (NOT A) = {3,7}