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Minimization: GATE and UGC NET

 

Q: UGC NET: 2013 (S2) question: 26

Match the following identities/laws to their corresponding name:

List-I                                                   

A. X + X = X                                 

     X.X = X

B. X + 0 = X                                 

     X.1 = X

C. X + 1 = 1                                 

     X.0 = 0

D. X(X + Y) = X                           

 

List – II

1. Dominance

2. Absorption

3. Idempotent

4. Identity

 

 

Before see the answer please follow chapter: Laws of Boolean Algebra

 

Solution:

 

 

A → 3, B → 4, C → 1, D → 2

 

∴ Option (a) is correct answer.

 

 

Q: GATE CSE 2004 question: 17

A Boolean function x’y’  + xy + x’y  is equivalent to

(a) x’ + y’                       

(b) x + y

(c) x + y’                       

(d) x’ + y 

 

Before see the answer please follow chapter: 

Laws of Boolean Algebra, Minimization by Boolean Laws, Types of Minimization Questions 

 

Solution:

 

Option (d) is correct answer.

 

 

Q: GATE CSE 2007, question: 33

Define the connective * for the Boolean variables X and Y as X*Y=XY+X’Y’, 

Let Z=X*Y.

Consider the following expression P, Q and R.

P: X=Y*Z     Q: Y=X*Z   R: X*Y*Z=1

 

Which of the following is true?

(a) Only P and Q are valid.

(b) Only Q and R are valid.

(c) Only P and R are valid

(d) All P, Q, R are valid.

 

Before see the answer please follow chapter: 

Laws of Boolean Algebra, Minimization by Boolean Laws, Types of Minimization Questions 

 

Solution:

P: 

 

Q:

 

R:

 

Option  (d) is correct answer.

 

Q: UGC NET 2016 (J2) Question: 9

The simplified form of a Boolean equation

 

Solution:

 

Option  (a) is correct answer. 

 

Q: GATE CSE 2008, Question: 26

If P, Q, R are Boolean variables, then

simplifies to

 

Before see the answer please follow chapter: 

Laws of Boolean Algebra, Minimization by Boolean Laws, Types of Minimization Questions 

 

Solution:

 

Option (a) is correct answer.

 

Q: GATE CSE 2014

Consider the following Boolean expression for F:

F(P, Q, R, S) = PQ + P’QR + P’QR’S

The minimal sum-of-product form of F is

(a) PQ + QR + QS       

(b) P + Q + R + S

(c) P’ + Q’ + R’ + S’      

(d) P’R + P’R’S + P

 

Before see the answer please follow chapter: 

Laws of Boolean Algebra, Minimization by Boolean Laws, Types of Minimization Questions, SOP and POS

 

Solution:

 

 

 

 

Option (a) is correct answer.