The Problem can be solved by Properties of Boolean Algebra or we also can use Consensus Theorem (also known as Redundancy Theorem in many literature)
Using Properties of Boolean Algebra
Now, Consensus Theorem provides a neat and quick solution just by observing few things :
If, following requirements are fulfilled.
- Three variables are there in Expression.
- Each variable is repeated twice. (Either in Normal Form or in Complement Form)
- One variable is repeated in complemented form (say X)
Reject the term which doesn't contain X.
In given problem, $xy+x′z+yz$
- A. Three Variables are there ($x, y$ and $z$)
- $x$ is repeated Twice ($x$ and $x'$), $y$ is repeated twice ($y$ and $y$) and $z$
is repeated twice ($z$ and $z$)
- $x$ is repeated in complemented form.
Therefore, reject term which doesn't contain $x$. Thus $yz$ is rejected.
Using same theorem $A'B'+AC'+B'C$ will be reduced to $A'B'+AC'$