Simplify x'z+yz'+x'y?

Question

Given:

$$x'z+yz'+x'y$$

How can I simplify it to:

$$x'z+yz'$$

I tried:

$$\begin{aligned} x'z+yz'+x'y &= x'(z+y)+y(z'+y) \\ &=x'z+(x'y+y) \\ &=x'z+y(x'+1) \\ &=x'z+y \end{aligned}$$

Are my calculations correct if so how can I reach what I wanted without using my calculations?

Answer 1

The x’y term is redundant, so it can be removed—but why?

Consider just x’z + yz’. Assume this statement is true. Then either x’z or yz’ is true. Since x only appears in the first product term and y only appears in the second, we know that either x is false or y is true or both. Therefore the x’y term in the original expression is redundant since it came as a consequence of x’z + x’y’.

You can also derive the result using a Karnaugh map.