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GO Classes DPP | Digital logics | Boolean Algebra

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3 3 votes

Select the Boolean function(s) equivalent to $x+y z$, where $x, y$, and $z$ are Boolean variables, and + denotes logical OR operation.

  1. $x+z+x y$
     
  2. $(x+y)(x+z)$
     
  3. $x+x y+y z$
     
  4. $x+x z+x y$

3 Answers

1 1 vote
  1. $x+z+x y=x(1+y)+z=x+z$
     
  2. $(x+y)(x+z)=x+x z+x y+y z=x(1+y+z)+y z=x+y z$
     
  3. $x+x y+y z=x(1+y)+y z=x+y z$
     
  4. $x+x z+x y=x(1+z+y)=x$
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