Stuck at simplifying boolean expression

Question

I'm getting stuck at the following boolean expression.

$$z + (x'y) + (xy') + (xt') + (yt')$$

In my solutions it's simplified and the $(yt')$ term is gone. How do they simplify this? I really cant see it....

Many thanks!

Answer 1

This comes from the Consensus Theorem. Notice that: \begin{align*} x'y + xt' + yt' &= x'y + xt' + (1)yt' \\ &= x'y + xt' + (x + x')yt' \\ &= x'y + xt' + (xyt' + x'yt') \\ &= (x'y + x'yt') + (xt' + xyt') \\ &= x'y(1 + t') + xt'(1 + y) \\ &= x'y(1) + xt'(1) \\ &= x'y + xt' \\ \end{align*}