Final answer:
To simplify the expression A'(A + B) + (B + AA)(A + B'), we use Boolean algebra rules, resulting in the expression simplifying to BA.
Step-by-step explanation:
The student's question asks to simplify the expression A'(A + B) + (B + AA)(A + B'). This expression involves the application of Boolean algebra rules, specifically the inverse, identity, distributive, commutative, and associative laws. However, the given information appears to pertain to various unrelated topics including vector multiplication, stoichiometry, and properties of real and complex numbers.
To address the question directly:
- A'(A + B) simplifies to 0 by the complement and the identity laws since A' is the complement of A, and AA' equals 0.
- (B + AA) simplifies to B because AA equals A and B + A equals B if A can be ignored. However, as A is not a simplifiable term in a Boolean context we treat it as A.
- Therefore, (B + AA)(A + B') simplifies to BA + BB' or BA because BB' equals 0.
Combining the simplified forms of the two expressions, we get 0 + BA, which ultimately simplifies to BA.