Final answer:
The question requires selecting two correct reduced forms of a boolean equation from a given list. Following boolean algebra principles, two possible correct reduced forms are B. Y(A, B, C, D) = A'B'D + C D' + B D' and
C. Y(A, B, C, D) = A'B'D + C'D + B D
Step-by-step explanation:
The question concerns reducing a boolean equation to its simplest forms. Two reduced forms of the given equation Y(A, B, C, D) are requested. Reduction of boolean equations generally involves applying laws and theorems of boolean algebra such as the commutative, associative, distributive, absorption, and De Morgan's theorems to simplify the given expressions.
Given that Y represents the output of a boolean function and A, B, C, D represent boolean variables or inputs, the task is to identify the two simplest forms of this equation. Let's consider terms given in the original question basis on common boolean simplification techniques:
- Term A'B'D is present in all options and can be seen as a part of the reduced equations.
- B'C is a reduced term where B and C are not complemented to each other, making it a potential part of the simplified equation.
- C D' is a term that is the complement of B'C, suggesting it could be a term in the simplified equation (option B).
- Looking at term B D', it is the complement of A'B'D, and thus cannot be part of the same sum of products equation. Therefore, option A is likely incorrect.
- Options involving redundancies or non-simplified terms (like B DD) are incorrect by the nature of boolean reduction.
Without knowing the exact process used to derive the equation or additional context, it's not possible to definitively select the correct forms. However, based on boolean simplification rules, we can infer the potential correct reduced forms of the equation Y(A, B, C, D) could likely be the ones not containing redundant or conflicting terms (like in options A and D), namely option B: Y(A, B, C, D) = A'B'D + C D' + B D' and option C: Y(A, B, C, D) = A'B'D + C'D + B D.