Q132 / 155 · WBJEE 2022 · Physics

The expression $\bar{A}(A+B)+(B+A A)(A+\bar{B})$ simplifies to

  • Correct answer
    A
    $A+B$
  • B
    $A B$
  • C
    $\overline{\mathrm{A}+\mathrm{B}}$
  • D
    $\bar{A}+\bar{B}$

Solution

$\begin{aligned} & \bar{A}(A+B)+(B+A A)(A+\bar{B}) \\=& \bar{A} A+\bar{A} B+(B+A)(A+\bar{B}) \\=& O+\bar{A} B+A B+A+B \bar{B}+A \bar{B} \\=&(\bar{A}+A) B+A+O+A \bar{B} \\=& 1 . B+A(1+\bar{B}) \\=& A+B \end{aligned}$

Hence, the correct answer is option: 'A'.

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