The Gateway to Computer Science Excellence

First time here? Checkout the FAQ!

x

+23 votes

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?

- (S1)-False, (S2)-True, (S3)-True, (S4)-False
- (S1)-True, (S2)-False, (S3)-False, (S4)-True
- (S1)-False, (S2)-False, (S3)-True, (S4)-True
- (S1)-True, (S2)-True, (S3)-False, (S4)-False

+24 votes

Best answer

+8 votes

$F = P{}' + QR$

for SOP we have :

$F = P{}.1.1 + 1.QR'=P{}'(Q+Q{}')(R+R{}') + (P+P{}')QR$

$P{}'QR + P{}'QR{}' +P{}'Q{}'R+P{}'Q{}'R{}'+PQR+P{}'QR$

$P{}'QR + P{}'QR{}' +P{}'Q{}'R+P{}'Q{}'R{}'+PQR$

$F=\sum(0, 1, 2, 3, 7)$ (**considering barred terms as 0 and unbarred as 1 and converting them to binary and then to decimal**).

now for POS we have :

$F = P{}' + QR = (P{}'+Q)(P{}'+R) = (P{}'+Q+0)(P{}'+R+0)$

$(P{}'+Q+R.R{}')(P{}'+R+Q.Q{}') $

$(P{}'+Q+R)(P{}'+Q+R)(P{}'+Q+R{}')(P{}'+Q{}'+R)$

$(P{}'+Q+R)(P{}'+Q+R{}')(P{}'+Q{}'+R)$

$F=\prod (4, 5, 6)$(**considering barred terms as 1 and unbarred as 0 and converting them to binary and then to decimal**).

- All categories
- General Aptitude 1.6k
- Engineering Mathematics 7.3k
- Digital Logic 2.7k
- Programming & DS 4.9k
- Algorithms 4.2k
- Theory of Computation 5.4k
- Compiler Design 2.1k
- Databases 4k
- CO & Architecture 3.5k
- Computer Networks 4.2k
- Non GATE 1.4k
- Others 1.5k
- Admissions 570
- Exam Queries 566
- Tier 1 Placement Questions 23
- Job Queries 70
- Projects 18

48,756 questions

52,850 answers

183,548 comments

68,742 users