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Prove algebraically that X + X’Y = X + Y.

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L.H.S.  = X + X’Y

= X.1 + X’Y    (X . 1 = X property of 0 and 1) 

= X(1 + Y) + X’Y   (1 + Y = 1 property of 0 and 1) 

= X + XY + X’Y

= X + Y(X + X’)

= X + Y.1   (X + X’ =1 complementarity law)

= X + Y   (Y . 1 = Y property of 0 and 1)

= R.H.S. Hence proved

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