(A'B' + AB)(A'B + AB')(A + B)
Max Function
Statistical function is of many categories. One of them is a MAX function. The MAX function returns the largest value from the list of arguments passed to it. MAX function always ignores the empty cells when performing the calculation.
Power Function
A power function is a type of single-term function. Its definition states that it is a variable containing a base value raised to a constant value acting as an exponent. This variable may also have a coefficient. For instance, the area of a circle can be given as:
(A'B' + AB)(A'B + AB')(A + B)
Let's simplify the given expression using Boolean algebra:-
First, we can apply the distributive law to the first two terms:
(A'B' + AB)(A'B + AB')(A + B)
= (A'B'A' + A'BA)(A'B + AB') (A + B) // distribute A'B' over AB
= (A'A'B'B + A'BA'B + A'B'A' + ABA)(A + B') (A + B) // distribute A'B over AB'
= (0 + A'BA'B + A'B'A' + ABA)(A + B') (A + B) // A'A'B'B = 0 using A'A = 0 and B'B = 0
= (A'BA'B + A'B'A' + ABA)(A + B') (A + B) // identity law: 0 + X = X
Next, we can apply the distributive law again:
(A'BA'B + A'B'A' + ABA)(A + B') (A + B)
= (A'BA'B)(A + B') (A + B) + (A'B'A')(A + B') (A + B) + (ABA)(A + B') (A + B) // distribute over (A + B') and (A + B)
= (A'BA'BA + A'BA'BB' + ABA'A + ABA'B' + A'B'BA + A'B'BB' + ABA'A + ABA'B')(A + B) // distribute over (A + B)
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