Question

Download Solution PDF

Let # be a binary operator defined as

X # Y = X’ + Y’ where X and Y are Boolean variables.

Consider the following two statements.

(S1) (P # Q) #R = P# (Q # R)

(S2) Q # R = R # Q

Which of the following is/are true for the Boolean variables P, Q and R?

This question was previously asked in
GATE CS 2015 Official Paper: Shift 3
Attempt in App
View all GATE CS Papers >
  1. Only S1 is true
  2. Only S2 is true
  3. Both S1 and S2 are true
  4. Neither S1 nor S2 are true

Answer (Detailed Solution Below)

Option 2 : Only S2 is true
Free Tests
View all Free tests >
Free
GATE CS Full Mock Test
65 Qs. 100 Marks 180 Mins
Start Now

Detailed Solution

Download Solution PDF

∴ S1 is FALSE

But

∴ S2 is TRUE

Important Points 

𝑋  𝑌 = 𝑋′ + 𝑌′ = (𝑋.𝑌)'  

It is a NAND operation and NAND is commutative but not associative

Download Solution PDF
Latest GATE CS Updates

Last updated on Jan 8, 2025

-> GATE CS 2025 Admit Card has been released on 7th January 2025.

-> The exam will be conducted on 1st February 2025 in 2 shifts.

-> Candidates applying for the GATE CE must satisfy the GATE Eligibility Criteria.

-> The candidates should have BTech (Computer Science). Candidates preparing for the exam can refer to the GATE CS Important Questions to improve their preparation.

-> Candidates must check their performance with the help of the GATE CS mock tests and GATE CS previous year papers for the GATE 2025 Exam.

Exams Tests Super Practice

More Minimization of Boolean Expression Questions

Q1.What is the result of applying the complement law A + A' in Boolean algebra?
Q2.Let \(\mathrm{f}(\mathrm{~A}, \mathrm{~B})=\overline{\mathrm{A}}+\mathrm{B}\), Simplified expression for function f (f (x y, y), z) is :
Q3.What happens when a bit string is XORed with itself n times as shown below ? [B ⊕ (B ⊕ (B ⊕ (B ..........n times]
Q4.Which of the following is the complement of the boolean function. A'B + CD' + A'B + CD'
Q5.Consider the following statements: A. There exists a Boolean algebra with '5' elements. B. Every element of Boolean algebra has unique complement. C. If a Lattice 'L' is a Boolean algebra then 'L' is not relatively complemented. D. The direct product of two Boolean Algebras is also a Boolean algebra Choose the correct answer about the four statements given above.
Q6.Simplify the following using K-Map F(A, B, C, D) = ∑(0, 2, 5, 7, 8, 10, 13, 15) 
Q7.What would be yielded after simplifying the following Boolean expression: Y = \(\rm\overline{(A+\bar{B}+C)+(B+\bar{C})}\)
Q8.Consider the following in Boolean Algebra X: a ∨ (b ∧ (a ∨ c)) = (a ∨ b) ∧ (a ∨ c) Y: a ∧ (b ∨ (a ∧ c)) = (a ∧ b) ∨ (a ∧ c) a ∨ (b ∧ c) = (a ∨ b) ∧ c is satisfied if
Q9.A+  AB̅ + AB̅C + AB̅CD̅ simplifies to: 
Q10.For the given Boolean function F (x, y, z) = Σ(0, 2, 4, 5, 6) simplified output will be-

More Number Representations and Computer Arithmetic Questions

Q1.What is the 2's complement of the binary number 101110?
Q2.What is the result of applying the complement law A + A' in Boolean algebra?
Q3.Which of the following is the correct octal representation of the hexadecimal number 1A3?
Q4.What happens to the carry-out bit when subtracting two n-bit numbers using 2's complement and the result is positive?
Q5.Let \(\mathrm{f}(\mathrm{~A}, \mathrm{~B})=\overline{\mathrm{A}}+\mathrm{B}\), Simplified expression for function f (f (x y, y), z) is :
Q6.What happens when a bit string is XORed with itself n times as shown below ? [B ⊕ (B ⊕ (B ⊕ (B ..........n times]
Q7.Match the LIST-I with LIST-II LIST - I Boolean Algebra Law LIST - II Axioms A. Absorption Law I. a + 1 = 1 B. Bounded Law II. a + 0 = a C. Identity Law III. a * (b + c) = (a * b) + (a * c) D. Distributive Law IV. a + (a * b) = a Choose the correct answer from the options given below:
Q8.Which of the following is NOT an alphabet used to denote a hexadecimal number?
Q9.Which of the following is NOT a binary number? 
Suggested Test Series
View All >
GATE Mathematics & General Aptitude (Common for All) Test Series
92 Total Tests with 0 Free Tests
Start Free Test
ISRO Scientist Computer Science Mock Test
22 Total Tests with   1 Free Tests
Start Free Test

GATE CS Important Links

BooksSyllabusPreparation TipsPaper AnalysisCut OffPrevious Year Papers

More Digital Logic Questions

Q1.In a 3-to-8 decoder, how many outputs are active for any given input?
Q2.What is the 2's complement of the binary number 101110?
Q3.What is the difference between edge-triggering and level-triggering?
Q4.How many select lines are required for a 1-to-8 Demultiplexer?
Q5.If the input I = 1 and the select lines are S1 = 1, and S0 = 0, what will be the values of the four outputs in a 1-to-4 Demultiplexer?
Q6.Which of the following is a characteristic of serial binary adders?
Q7.How many distinct states are there are in an n-bit ring counter?
Q8.What is the result of applying the complement law A + A' in Boolean algebra?
Q9.Which of the following is the correct octal representation of the hexadecimal number 1A3?
Q10.Which Boolean expression correctly represents the Difference (D) output of a Full Subtractor?
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
support@testbook.com
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： teen patti star apk teen patti master app teen patti real cash apk