2. The followingboolean equations have been reduced from the left-hand-side to thatof the right-hand-

side by BooleanAlgebra. Use Venn Diagrams to show that the reductions arevalid.

(a) X(X + Y) = X

(b) X Y(w/ a baron top) +Y = X + Y

(c) (X + Y ) ( a bar onthe entire thing)= X(w/bar ontop)*Y(w/ bar on top)

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