Final Answer:
The equation in sum-of-minterms form among the options given is (d) ab'c + ab'c' + abc.
Step-by-step explanation:
The sum-of-minterms form represents a Boolean expression as a sum of minterms, where each minterm corresponds to a unique combination of variables. In this context, a minterm is a product term in which all variables appear exactly once, either complemented or uncomplemented.
To identify the sum-of-minterms form, let's break down the provided options:
a. ab + bc
This expression doesn’t represent the sum of minterms as it combines terms without covering all possible variable combinations.
b. ab'(c + c)
This expression can be simplified to ab' by applying the property of c + c' = 1. However, it doesn't represent a sum of minterms.
c. abc + ab'c + a'c'
This expression doesn't cover all possible minterms as it lacks the term ab'c'.
d. ab'c + ab'c' + abc
This expression covers all possible minterms: ab'c, ab'c', and abc, making it the equation in sum-of-minterms form. Each term represents a unique combination of variables, fulfilling the criteria of the sum-of-minterms form.
Therefore, option (d) ab'c + ab'c' + abc is the equation that best fits the sum-of-minterms form among the given options.