GATE-DLD-Boolean Algebra

The Boolean function A + BC is a reduced form of [GATE-EC-1997]

• AB + BC        

• .      (A + B)(A + C)        

• A’B + AB’C        

• (A + C)B

.       For the identity, AB + A’C + BC = AB + A’C, the dual form is [GATE-EC-1998]

• (A+B)(A'+C)(B+C)=(A+B)(A'+C)

• (A'+B' ) (A+C' )(B'+C')=(A'+B' ) (A+C^' )

• (A+B)(A'+C)(B+C)=(A'+B')(A+C')

• A'B'+ AC' + B'C' = A'B' + AC'

The logical expression Y = A + A’B is equivalent to [GATE-EC-1999]

• AB

• A'B

• A'+B

• A+B

• X

• Y

• XY

• X+Y

The following Boolean expression Y = A’B’C’D +  A’BCD’ + AB’C’D + ABC’D’      can be minimized to  [GATE-EC-2007]

• Y = A’B’C’D +  A’BC’ + AC’D

• Y = A’B’C’D +  BCD’ + AB’C’D

• Y = B’C’D +  A’BCD’ + AB’C’D

• Y = B’C’D +  A’BCD’ + ABC’D’

Select the Boolean function(s) equivalent to 𝑥 + 𝑦𝑧, where 𝑥, 𝑦, and 𝑧 are Boolean variables, and + denotes logical OR operation. [GATE-EC-2022]

• 𝑥 + 𝑧 + 𝑥𝑦

• (𝑥 + 𝑦)(𝑥 + 𝑧)

• 𝑥 + 𝑥𝑦 + 𝑦𝑧

• 𝑥 + 𝑥𝑧 + 𝑥𝑦