Morris Mano Edition 3 Exercise 4 Question 26 (Page No. 151)

Question

Prove that  $x \oplus 1$ = x’ and $x \oplus 0$ = x.

Answer 1

we know that ${\color{Magenta}{{x\oplus y}=x\overline{y}+\overline{x}y}}$

Now ${\color{Green}{{x\oplus 1}=x\cdot\overline{1}+\overline{x}\cdot1=x\cdot 0+\overline{x}=\overline{x}}}$

and ${\color{Blue}{{x\oplus 0}=x\cdot\overline{0}+\overline{x}\cdot0=x\cdot 1+0=x}}$

Answer 2

WE can solve using truth table