For multiple choice questions, you have to choose the best answer for each quest

Question

For multiple choice questions, you have to choose the best answer for each question unless stated otherwise. Each question is worth 5 points 1. Which of the following is the dual of the expression A +B C ? (Hint: You can apply distributive rule after taking the dual.) B. OA(B+C) D. O AB +AC E.(D (A + B) C 2. Which of the following is the simplified expression of (Hint: Apply principle of daulity, Do not forget to take the dual again after simplification in the dual space) B. OAB D. C) A + B, C E. OAB c What is the missing keywor Type your answer. which is case sensitive, in the blank (do NOT put in any punctuation mark) 4. Find the simplest boolean expression of the following map describing the four variables w x.y z. 00 01 11 10 01 1 D. Owx'y'z + xyz E. Onone of the above 5. Which of the best d the best a the

Explanation / Answer

1.

A + BC'

duality rules
+ -> .
. -> +
1 -> 0
0 -> 1

so

A.(B+C')
AB + AC' (distributive)

so option (D) is correct

2.

AB'(A+B+C)(A+B+C')(A+B'+C)(A'+B'+C')
AB'(A+B+CC')(A+B'+C)(A'+B'+C')
AB'(A+B)(A+B'+C)(A'+B'+C') complement,identity
(AAB'+ AB'B)(A+B'+C)(A'+B'+C') distributive
(AB' + A)(A+B'+C)(A'+B'+C') indempotent (for A'a), then complement and identity to remove BB'
A(B' + 1)(A+B'+C)(A'+B'+C')
A(A+B'+C)(A'+B'+C') identity
applying dualiy
A + (AB'C) + (A'B'C')
A(1+B'C) + (A'B'C') distributive
A + (A'B'C') identity
AA' + AB' + AC'
AB' + AC'
A(B' + C')
reversing duality
A + B'C'

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