simplify the expression (show the steps):
x= (~A)(~B)+AB+(~A)(~B)(~C)+AB(~C)+~((A+D)(B+C+D))+~(A+B)B
To simplify the expression, let's follow these steps:
Step 1: Distribute negation (~) over the brackets.
Step 2: Apply distributive property by multiplying terms within the brackets.
Step 3: Simplify the expression.
Given expression: x = (~A)(~B) + AB + (~A)(~B)(~C) + AB(~C) + ~((A+D)(B+C+D)) + ~(A+B)B
Step 1: Distribute negation (~) over the brackets
x = (~A)(~B) + AB + (~A)(~B)(~C) + AB(~C) + (~((A+D)(B+C+D))) + ~(A+B)B
Step 2: Apply distributive property
x = (~A)(~B) + AB + (~A)(~B)(~C) + AB(~C) + (~(A+D) + ~(B+C+D)) + ~(A+B)B
Step 3: Simplify the expression
x = (~A)(~B) + AB + (~A)(~B)(~C) + AB(~C) + (~A~D + ~B~C~D) + ~(A+B)B
Simplified expression: x = ~A~B + AB + ~A~B~C + AB~C + ~A~D + ~B~C~D + ~AB~B