GATE CSE 2015 Set 3 | Question: 44

Question

Given the function $F = P' +QR$, where $F$ is a function in three Boolean variables $P, Q$ and $R$ and $P'=!P$, consider the following statements.

$(S1) F = \sum(4, 5, 6)$

$(S2) F = \sum(0, 1, 2, 3, 7)$

$(S3) F = \Pi (4, 5, 6)$

$(S4) F = \Pi (0, 1, 2, 3, 7)$

Which of the following is true?

• A. (S1)-False, (S2)-True, (S3)-True, (S4)-False
• B. (S1)-True, (S2)-False, (S3)-False, (S4)-True
• C. (S1)-False, (S2)-False, (S3)-True, (S4)-True
• D. (S1)-True, (S2)-True, (S3)-False, (S4)-False

Comments

A is right option

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It is one of the most basic questions I have come across but couldn't figure out what exactly it meant. Anyone else who found this ambiguous?

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$f=\sum(0,1,2,3,7)$

$f=\Pi(4.5.6)$

Answer 1

Option A is correct

P'QR + P'QR' +P'Q'R + P'Q'R' + PQR = ⋿(0,1,2,3,7) = ∏(4,5,6)

Answer 2

option A is correct.

F=~P+QR

=011+000+010+001+011+111=∑(0,1,2,3,7)=Π(4,5,6)