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Given a function of a, b, and c, which equation is in sum-of-minterms form?

a. ab + bc
b. ab'(c + c)
c. abc + ab'c + a'c'
d. ab'c + ab'c' + abc

User Cechner
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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.

User Tilman
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