GATE 2011
October 18, 2023Boolean-Algebra
October 19, 2023Boolean-Algebra
| Question 1 |
The Boolean function x’y’ + xy + x’y is equivalent to
| x’ + y’ | |
| x + y | |
| x + y’ | |
| x’ + y |
Question 1 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 1 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
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