GATE 2011
October 18, 2023Digital-Logic-Design
October 19, 2023GATE 2004
|
Question 17
|
The Boolean function x’y’ + xy + x’y is equivalent to
|
x’ + y’
|
|
|
x + y
|
|
|
x + y’
|
|
|
x’ + y
|
Question 17 Explanation:
x’y’ + xy + x’y
= x’y’ + x’y + xy
= x'(y’+y)+xy
= x’⋅1+xy
= x’+xy
= (x’+x)(x’+y)
= 1⋅(x’+y)
= x’+y
= x’y’ + x’y + xy
= x'(y’+y)+xy
= x’⋅1+xy
= x’+xy
= (x’+x)(x’+y)
= 1⋅(x’+y)
= x’+y
Correct Answer: D
Question 17 Explanation:
x’y’ + xy + x’y
= x’y’ + x’y + xy
= x'(y’+y)+xy
= x’⋅1+xy
= x’+xy
= (x’+x)(x’+y)
= 1⋅(x’+y)
= x’+y
= x’y’ + x’y + xy
= x'(y’+y)+xy
= x’⋅1+xy
= x’+xy
= (x’+x)(x’+y)
= 1⋅(x’+y)
= x’+y