Test Index

MHT CET 2021 Physics Solved Paper

Question : 63 of 100

Marks: +1, -0

The output

Y

Solution:

Here,

\;\; Y' = \overline{A \cdot B} = \overline{A} + \overline{B}

Y'' = \overline{A \cdot (\overline{A}+\overline{B})} = \overline{A} + \overline{(\overline{A}+\overline{B})}

[By de Morgan's theorem]

= \overline{A} + (\overline{\overline{A}} \cdot \overline{\overline{B}}) = \overline{A} + (A \cdot B)

Y''' = \overline{B \cdot (\overline{A}+\overline{B})} = \overline{B} + \overline{\overline{A}+\overline{B}} = \overline{B} + (\overline{\overline{A}} \cdot \overline{\overline{B}})

= \overline{B} + (A \cdot B)

Y = \overline{Y'' \cdot Y'''} = \overline{\overline{A} + (A \cdot B) \cdot [\overline{B} + (A \cdot B)]}

= [\overline{\overline{A} + A \cdot B}] + [\overline{\overline{B} + (A \cdot B)}]

= \overline{\overline{A}} \cdot (\overline{A \cdot B}) + \overline{\overline{B}} \cdot (\overline{A \cdot B})

= A(\overline{A B}) + B(\overline{A B})

= (A+B)(\overline{A \cdot B}) = (A+B)(\overline{A}+\overline{B})

= A \overline{A} + A \overline{B} + B \overline{A} + B \overline{B}

= 0 + A \overline{B} + B \overline{A} + 0

= \overline{A} \cdot B + A \cdot \overline{B}

Go to Question:

Prev Question

Next Question