6. Recall the defining rules for elements x, y, and z in a Boolean Algebra B,...

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6. Recall the defining rules for elements x, y, and z in a Boolean Algebra B, i.e., that: (a) Identity: There exist elements 0, 1 E B such that for every x E B we have: x+0=x xol=x (b) Complement: For every x B, there is a unique element E B such that: x+x=1 xox=0 (c) Commutativity: For every x, y B, we have: x+y=y+x xoy=yox (d) Distributivity: For every x, y, z E B, we have: xo (y+2)=xoy+xoz (x+y)o(x+2)=x+yoz Use these rules to show the Idempotent Rules for any x B. i.e. : 6. Recall the defining rules for elements x, y, and z in a Boolean Algebra B, i.e., that: (a) Identity: There exist elements 0, 1 E B such that for every x E B we have: x+0=x xol=x (b) Complement: For every x B, there is a unique element E B such that: x+x=1 xox=0 (c) Commutativity: For every x, y B, we have: x+y=y+x xoy=yox (d) Distributivity: For every x, y, z E B, we have: xo (y+2)=xoy+xoz (x+y)o(x+2)=x+yoz Use these rules to show the Idempotent Rules for any x B. i.e. :