Question

Consider the equation f = a(b c) (d’) ac’ (b d). a) convert f to the shortest sum-of-products form. A. a'b'cd + ab'c'd + a'bcd' + abcd

B. a'b'c'd' + ab'c'd' + a'b'cd + ab'cd'

C. a'b'cd' + ab'cd' + a'bcd + abcd'

D. a'b'cd' + ab'c'd' + a'b'cd + ab'cd'

Answer 1

The expression f cannot be simplified to match any of the given options using the distributive law, and thus none of the presented options A, B, C, or D are correct.

Step-by-step explanation:

To convert the given expression f = a(b + c) (d’) + ac’ (b + d) to the shortest sum-of-products form, we must apply the distributive law. The distributive law states A(B + C) = AB + AC. Let's apply this law to both parts of the expression.

For the first part a(b + c)(d’), we get:

ad’(b + c)

abd’ + acd’

For the second part ac’(b + d), we get:

ac’b + ac’d

abc’ + acd'

Merging both parts, we have abd’ + acd’ + abc’ + ac’d. To reach a sum-of-products form that cannot be further simplified, you must look at the options given and identify any cases where terms can be omitted due to redundancy or common factors. The fact that none of the terms share a common literal that would allow further simplification means we have reached the shortest SOP form.

Therefore, the correct answer is not provided in the options as our final expression does not match any of the given options.