# Prove the identity in this boolean equation

$$AD'+A'B+C'D+B'C=(A'+B'+C'+D')(A+B+C+D)$$

Don't know where to begin with this.

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By the same reasoning the LHS could be $XY'+YZ'+ZT'+TX'$ as soon as $\{X,Y,Z,T\}=\{A,B,C,D\}$ since this also encodes the set [no unanimity amongst $X$, $Y$, $Z$, $T$] which obviously coincides with [no unanimity amongst $A$, $B$, $C$, $D$]. –  Did Feb 20 '13 at 7:01