Question

Which of the following expression is equivalent to

$(A\oplus B)\oplus C?$

• A. $(A+B+C)(\overline{A}+\overline{B}+\overline{C})$
• B. $(A+B+C)(\overline{A}+\overline{B}+C)$
  
• C. $ABC+\overline{A}(B\oplus C)+\overline{B}(A\oplus C)$
• D. None of these

Answer 1

The correct option is C

$ABC+\overline{A}(B\oplus C)+\overline{B}(A\oplus C)$

$(A\oplus B)\oplus C=(A\overline{B}+B\overline{A})\oplus C$

$=(A\overline{B}+B\overline{A})\overline{C}+\left(\overline{A\overline{B}+B\overline{A}}\right)C$

$=A\overline{B}\overline{C}+\overline{A}B\overline{C}+\left[\right(\overline{A}+B\left)\right(A+\overline{B}\left)\right]C$

$=A\overline{B}\overline{C}+\overline{A}B\overline{C}+\overline{A}\overline{B}C+ABC$

$=ABC+\overline{A}(B\oplus C)+\overline{B}(A\oplus C)$