Database-Management-System
October 3, 2023GATE 2023
October 3, 2023JNU PhD CS 2019
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Question 10
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The number of min-terms after minimizing the following Boolean expression is
[D’ + AB’ + A’C + AC’D + A’C’D]’
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1
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46
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56
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76
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Question 10 Explanation:
(D’ + AB’ + A’C + AC’D + A’C’D)’
(D’ + A’C’D + AB’ + A’C + AC’D)’
((D’ + D) (D’ + A’C’) + AB’ + A’C + AC’D)’
(D’ + A’C’ + AB’ + A’C + AC’D)’
(D’ + AC’D + AB’ + A’(C + C’))’
(D’ + AC’ + AB’ + A’)
(D’ + AC’ + (B’ + A’) (A + A’)
(D’ + AC’ + B’ + A’)
(D’ + (A + A’) (C’ + A’) + B’)’
(D’ + C’ + A’ + B’)’ = ABCD
(D’ + A’C’D + AB’ + A’C + AC’D)’
((D’ + D) (D’ + A’C’) + AB’ + A’C + AC’D)’
(D’ + A’C’ + AB’ + A’C + AC’D)’
(D’ + AC’D + AB’ + A’(C + C’))’
(D’ + AC’ + AB’ + A’)
(D’ + AC’ + (B’ + A’) (A + A’)
(D’ + AC’ + B’ + A’)
(D’ + (A + A’) (C’ + A’) + B’)’
(D’ + C’ + A’ + B’)’ = ABCD
Correct Answer: A
Question 10 Explanation:
(D’ + AB’ + A’C + AC’D + A’C’D)’
(D’ + A’C’D + AB’ + A’C + AC’D)’
((D’ + D) (D’ + A’C’) + AB’ + A’C + AC’D)’
(D’ + A’C’ + AB’ + A’C + AC’D)’
(D’ + AC’D + AB’ + A’(C + C’))’
(D’ + AC’ + AB’ + A’)
(D’ + AC’ + (B’ + A’) (A + A’)
(D’ + AC’ + B’ + A’)
(D’ + (A + A’) (C’ + A’) + B’)’
(D’ + C’ + A’ + B’)’ = ABCD
(D’ + A’C’D + AB’ + A’C + AC’D)’
((D’ + D) (D’ + A’C’) + AB’ + A’C + AC’D)’
(D’ + A’C’ + AB’ + A’C + AC’D)’
(D’ + AC’D + AB’ + A’(C + C’))’
(D’ + AC’ + AB’ + A’)
(D’ + AC’ + (B’ + A’) (A + A’)
(D’ + AC’ + B’ + A’)
(D’ + (A + A’) (C’ + A’) + B’)’
(D’ + C’ + A’ + B’)’ = ABCD
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