 Consensus theorem

In Boolean algebra, the product $yz$ is the consensus of $xy$ and $\bar{x}z$. If $yz=1$, either $x=1$ and $xy=1$, or $x=0$ and $\bar{x}z=1$, so adding the consensus does not change the Boolean function. It can change a circuit's transient behavior: while $x$ switches, the two original product terms may briefly both be zero because of unequal propagation delays, but $yz$ remains one. Keeping the logically redundant consensus product can therefore remove a static-one logic hazard.

The Consensus theorem is a simplification rule used in Boolean algebra and digital logic design. It states that certain combinations of Boolean variables can be simplified, leading to more efficient expressions.