Question

Which of the following statements is NOT true?

a) A+(A⋅B) = A(A+B)
b) A⋅B+A'⋅B'= 1
c) (AB)'= A'+ B'
d) A'⋅B + B' = A'+ B'
e) (A+1) = 1

Answer 1

The statement (d) A' ⋅B + B' = A'+ B' is NOT true according to Boolean algebra. The correction applies the distributive law: A'+B'.

Step-by-step explanation:

The question asks to identify which of the given statements is NOT true. These statements pertain to properties of Boolean algebra, which is often a topic in computer science or digital logic courses. Here are the evaluations of each statement:

• a) A+(A⋅B) = A - This statement is using the absorption law, which is correct, but the equal sign is improperly used, as the correct expression should be A+(A⋅B) = A.
• b) A⋅B+A' ⋅B'= 1 - This is a version of the complement law and is true because either A or not-A will be true, and the same goes for B, so the entire expression will always be true (equals 1).
• c) (AB)'= A'+ B' - This is De Morgan's theorem and is correctly stated.
• d) A' ⋅B + B' = A'+ B' - This statement is incorrect. Using the distributive law, it should be A'+B', not A'⋅B + B'.
• e) (A+1) = 1 - This is true because anything ORed with 1 is always 1.

Therefore, the statement (d) A' ⋅B + B' = A'+ B' is NOT true. The correction would be to apply the distributive law correctly: A'+B'.